HIGHER SECONDARY FIRST YEAR MATHEMATICS

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Eugene Wheeler
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1 HIGHER SECONDARY FIRST YEAR MATHEMATICS ANALYTICAL GEOMETRY Creative Questions Time :.5 Hrs Marks : 45 Part - I Choose the orret answer 0 = 0. The angle between the straight lines 4y y 0 is a) 0 30 b) 0 45 ) d) 90. If the sum of the slopes of the lines given by y 7 y 0 is four times their produt, then has the value a) b) ) d) 3. A straight line passing through the point A (3, 4) is suh that its interept between the aes is biseted at A. Then its equation is a) 3 4 y 7 0 b) 4 3y 4 ) 3 4y 5 d) y 7 4. If the line y k passes through the point whih divides the line segment joining the points (, ) and (, 4) in the ratio 3 : then k equals 9 a) b) ) 5 d) If the lines 3 4 y 7 0 and 3 y 5 0 are two diameters of a irle of area 49 square units the equation of the irle is a) y y 6 0 b) y y 6 0 ) y y 47 0 d) y y The point diametrially opposite to the point (, 0) on the irle y 4 y 3 0 a) ( 3, 4) b) (3, 4) ) ( 3, 4) d) ( 3, 4 ) 7. The number of ommon tangent to the irle y 4 6 y 0 and y 6 8 y 6 0 is a) 3 b) 4 ) d) 8. The equations of the three sides of a triangle are =, y + l = 0 and + y = 4. The o-ordinates of the irumentre of the triangle are a) ( 4, 0) b) (, ) ) ( 0, 4) d) None of these

2 9. If the sum of the slopes of the lines given by 4 y 7 y 0 is equal to the produt of the slopes, then = a) 4 b) 4 ) d) 0. If the lines a + by + = 0, b + y + a = 0 and + ay + b = 0 are onurrent ( a b 0) then a) a b 3ab 0 b) a b ) a b b a ab 0 Part - II d) All the above Answer any three of the following questions 3 = 6. If one of the lines given by 6 y 4y 0 is 3 4 y 0 then find C. Find the equation of the irle passing through the points (, 0) and (0. ) and having the smallest radius. 3. The o-ordinates of the middle points of the sides of a triangle are (4, ), (3, 3) and (, ), then find the o-ordinates of its entroid. 4. Find the inlude an angle of the diagonals of the parallelogram whose sides are l + my + n = 0, l + my + k = 0, m + ly + n = 0, m + ly + k = 0 5. Find the equation of the irle having diameters y 3 0, 4 3 y 0 and radius equal to Part - III Answer any three of the following questions 3 3 = 9 6. Find the equation of the straight line passing through the point (4, 3) and making interepts on the oordinate aes whose sum is y 7. The line L given by passes through the point (3, 3). The line K is parallel 5 b to L and has the equation y 3, then find the distane between L and K. 8. If the two irles ( ) ( y 3) r and y 8 y 8 0 interset in two distint points, then prove that r 8

3 9. The two irles y a and y ( 0 ) touh eah other, then show that a 0. Find the length of the diameter of the irle whih touhes the -ais at the point (, 0) and passes through the point (, 3) Part - IV Answer any four of the following questions 4 5 = 0. Find the distane between a pair of straight lines 9 4y 6 y 6 y 0. Let PS be the median of the triangle with verties P(, ), Q(6, ), and R(7, 3). then find the equation of the line passing through (, ) and parallel to PS 3. In a ABC, side AB has the equation + 3y = 9 and the side AC has the equation + y = 6. If the mid point of BC is (5, 6) then find the equation of BC 4. If the angle between the two lines represented by 5y 3 y 6 7 y 4 0 is tan ( m), then find m. 5. Find the equation of irle passing through (3, 6 ) and touhing both the aes. ***** T. Ayyanar, M.S., B.Ed., D.P.Teh Instrutor (Mathematis) SBGGHSS, Puduherry akarthik04@gmail.om Cell:

4 Q.No Options 3 b 4 d 5 6 HIGHER SECONDARY FIRST YEAR MATHEMATICS ANALYTICAL GEOMETRY Creative Questions Answers and Solutions Part - I 7 a 8 a 9 0 d Part II. 6 y 4y (3 4 y)( ky) Comparing the oeffiient of y and y 3k 8 4k 4 k 3 3 k. If these (, 0), (0, ) points lie anywhere on the irumferene but diametrially opposite eah other Equation of irle is )( ) ( y y )( y y ) 0 ( ( )( 0) ( y 0)( y ) 0 y y 0

5 3. The entroid of a triangle and the entroid of triangle formed by joining mid points of the original triangle will oinide. Centroid = 3 y y y, =, = 3, 3 4. Sine the equations differ only by the onstant term The given lines are parallel It is rhombus The diagonals of rhombus interset at right angle 3 5. To find the entre, Solve y 3 0, 4 3 y 0 Centre = (, ) r = Equation of irle ( h) ( y k) r ( ) ( y ) Part III y 6. The equation of the straight line => a b Given a b b a a y a ( a) ay a( a) It passes through the point (4, 3)

6 ( a)4 3a a a 4 a a a 4 a a When a = When a = b = 3 b = The equations of straight lines y 3 or y y 7. 5 b b 5 y 5b It passes through the point (3, 3) b( 3) 5(3) 5b 3b 60 5b b y 00 4 y 0 4 y 0 0 Slope y 3 3 y 3 m 3 m a b m 4 In parallel lines slopes are equal m m

7 3 3 y 4 4 y y3 0 Distane between the two parallel lines y = ( ) 8. ( ) ( y 3) r Centre C = (, 3) radius r = r y 8 y 8 0 g = 8 f = = 8 g = 4 f = Centre C = (4, ) radius r = ( 4) 8 r = 3 ( 4) (3 ) = 9 6 = 5 Condition for irles to interset at two plaes = r r r r r 3 5 r 3 r 8 9. y a 0 g = a f = 0 a g = a, 0

8 a r 0 0 r = a y Centre C = (0, 0) radius r = a 0 0 a 0 Cirles touh eah other r r a a = a a ( 0) 0. Cirles touhes -ais at (, 0) Let the entre of the irle be (, h) CA = CB h r ( ) ( h h 6h 9 6h h 6 3) Length of the diameter = 0 6 = 0 3 Part IV. 9 4y 6 y 6 y 0 9 4y 6 y = ( 3 4 y) (3 4 y) 9 4 y 6 y 6 y ( 34yl) (34ym) Comparing the oeffiient of y and onstant

9 3m 3l lm m l 4 solve the equations m 6, m l m When m = 6 When m = l = l = 6 The equations are 3 4 y 0 and 3 4 y Distane between the lines 3 4 = Midpoint of S =, 3 =, y y Equation of PS y y y 3 9 y 9 9 y 0 Equation of straight line whih is parallel to PS 9 y k 0 It passes through (, ) () 9( ) k 0 k = 7 The required equation is 9 y 7 0 A 3. Let the verties be B, ) and C, y ) ( y Given: Midpoint of BC = (5, 6) y y, (5, 6) ( B (, y D C (, y ) (5, 6) )

10 = 0 and y y = 0, y y C 0, y Point B lie on the AB 3 y 9 Point C lie on the AC Solve and 0 ( y) 6 y 8 B( 4, 7), C(6, 4 and y 7 5) Equation of BC 4 7 y ( 4) ( y 7) y 4. 5y 3 y 6 7 y 4 0 5y 3 y 3y y = 5 y 3 y 6 7 y 4 3 y l y m Comparing the oeffiient of and y m l 6 3m l 7 Solving we get l 4, m The equations are 3 y 4 0, y 0 Slope m, Slope m 3 Angle between two straight lines tan m m m m = 3 3

11 = tan 5 m 5 5. If the irle touhes the both aes then h = k = r (radius of the irle) Equation of the irle ( h) ( y k) r ( r) ( y r) r It passes through the point (3, 6) ( 3 r) (6 r) r r 8r 45 0 ( r 5) ( r 3) 0 When r = 3 The equation of irle is ( 3) ( y 3) 3 y 6 6 y 9 0 When r = 5 The equation of irle is ( 5) ( y5) 5 y 30 30y 5 0 **** T. Ayyanar, M.S., B.Ed., D.P.Teh Instrutor (Mathematis) SBGGHSS, Puduherry akarthik04@gmail.om Cell:

12 th Maths Way to Success

12 th Maths Way to Success th Maths Quarterly Eam-7-Answer Key Part - A Q.No Option Q.No Option Q.No Option Q.No Option 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 Part B. A adj A A adja..() adja A () A I () From (), (),() we get A adja adja