SET I. If the locus of the point of intersection of perpendicular tangents to the ellipse x a circle with centre at (0, 0), then the radius of the circle would e a + a /a ( a ). There are exactl two points on the ellipse x a are equal and equal to a Ahijit Kumar Jha is a whose distance from the center of the ellipse. Eccentricit of this ellipse is equal to. If the line = mx + c, interests the ellipse x a, at points whose eccentric angles differ /, then (a m + ) = 4c (a + m ) = 4c a m + = 4c a + m = 4c 4. Consider an ellipse with major and minor axes of length 0 and 8 units respectivel. The radius of largest circle that can e inscried in this ellipse, it is given that centre of this circle is one focus of the ellipse, is equal to 4 units units 6 units none of these. Eccentricit of the ellipse x + 6x + = 8 is 6. The tangent at the point '' on the ellipse x + = meets the auxiliar circle in two a points which sutends a right angle at the centre, then the eccentricit 'e' of the ellipse is given the equation e ( + cos ) = e. (cosec ) = e ( + sin ) = e ( + tan ) = 7. S and T are the foci of an ellipse and B is an end of the minor axis. If STB is equilateral, then e is http://akj9.wordpress.com
/4 / / none of these Ahijit Kumar Jha 8. A ladder units long slides in a vertical plane with its ends in contact with a vertical wall and a horizontal floor along x-axis. The locus of a point on the ladder 4 units from its foot has the equation : x 4 + = x = 6 64 x = x + 64 6 4 = 9. Eccentric angle of a point on the ellipse x + = 6 at a distance units from the centre of the ellipse is / / / 4 none of these 0. The point of intersection of the tangents at the point P on the ellipse x a corresponding point Q on the auxiliar circle meet on the line : x = a/e x = 0 = 0 none of these. If and are eccentric angles of the ends of a focal chord of the ellipse x a tan tan e e e e is equal to e e e e = and its, then. The distances from the foci of P(a, ) on the ellipse x 9 are 4 4 a 4 4 none of these. If tan. tan = a x then the chord joining two points & on the ellipse a http://akj9.wordpress.com
will sutend a right angle at focus end of the major axis centre end of the minor axis Ahijit Kumar Jha 4. The equations of the common tangents to the ellipse, x + 4 = 8 & the paraola = 4x are x = ± x 4 = ± x + 4 = ± none of these. If O is the centre, OA the semimajor axis and S the focus of an ellipse, the eccentric angle of an point P is POS PSA PAS none of these 6. If A and B are two fixed points and P is a variale point such that PA + PB = 4, the locus of P is a paraola an ellipse a hperola none of these F HG 7. If P( ) and Q I K J are two points one the ellipse x a x x a a x a 4 none of these, locus of mid-point of PQ is 8. The length of the chord of the ellipse x where mid-point is 6 0 806 0 86 0 none of these F HG, 9. The sum of the square of perpendiculars on an tangent to the ellipse x from two point a on the minor axis, each at a distance are from the centre, is a a + a - 0. If latus rectum of the ellipse x tan sec is / then ( 0 ) is equal to / / 6 / 8 none of these I K J http://akj9.wordpress.com
SET II Ahijit Kumar Jha. The length of the major axis of the ellipse (x 0) + ( + ) = 0 0 7 0 (x 4 7) 4 4 is. The tangent and normal to the ellipse x + 4 = 4 at a point P( ) on it meets the major axes in Q and R respectivel. If QR =, then cos is equal to 4 none of these. x The ellipse and the straight line = mx + c intersect in real points onl if a a m < c a m > c a m c c 4. The foci of the ellipse (x + ) + 9 ( + ) = are at (, ) and (, 6) (, ) and (, 6) (, ) and (, ) (, ) and (, 6).. The parametric representation of a point on the ellipse whose foci are (, 0) and (7, 0) and eccentricit / is ( + 8cos, 4 sin ) (8cos, 4 sin ) ( + 4 cos, 8sin ) none of these 6. x The equation =, will represent an ellipse if 6 a a a (, ) a(, 6) a (, ) (6, ) a (, 6) ~ {4} 7. Tangents are drawn to the ellipse x + = 4 from an aritrar point on the line x + = 4, the corresponding chord of contact will alwas pass through a fixed point, whose coordinates are,, 8. The line = x touches the ellipse x + 4 =, at,, http://akj9.wordpress.com
, Ahijit Kumar Jha (, ) (, ) None of these x 9. The normal drawn to the ellipse at the extremit of the latus rectum passes through the a extremit of the minor axis. Eccentricit of this ellipse is equal to x 0. The line x = 8 is a normal to the ellipse. If e the eccentric angle of the foot 9 of this normal, then is equal to None of these 6 4 x. Tangent drawn to the ellipse at point P meets the coordinate axes at points A and B a respectivel. Locus of mid-point of segment AB is x a a x 4 4 a x x a x. Tangents PA and PB are drawn to the ellipse from the point P(0, ). Area of triangle 6 9 PAB is equal to 6 6 04 sq. units sq. units sq. units sq. units x. Tangents are drawn to the ellipse from an point on the paraola = 4x. The 6 9 corresponding chord of contact will touch a paraola, whose equation is + 4x = 0 = 4x + 9x = 0 = 9x 4. The normal at a variale point P on an ellipse x = of eccentricit e meets the axes of the a ellipse in Q and R then the locus of the mid-point of QR is a conic with an eccentricit e such that e is independent of e e = e = e e = /e http://akj9.wordpress.com
Ahijit Kumar Jha. An ellipse is such that the length of the latus rectum is equal to the sum of the lengths of its semi principal axes. Then ulges to a circle ecomes a line segment etween the two foci ecomes a paraola none of these 6. If the line x + 4 = 7 touches the ellipse x + 4 = then, the point of contact is 7, 7, 7, 7 none of these 7. A common tangent to 9x + 6 = 44 ; x + 4 = 0 & x + x + = 0 is = x = 4 x = 4 = 8. If F & F are the feet of the perpendiculars from the foci S & S of an ellipse x = on the tangent at an point P on the ellipse, then (S F ). (S F ) is equal to 4 9. The area of the rectangle formed the perpendiculars from the centre of the standard ellipse to the tangent and normal at its point whose eccentric angle is /4 is a a a a a a a a a a a a 0. If & are the eccentric angles of the extremities of a focal chord of an standard ellipse, then the eccentricit of the ellipse is : cos cos cos( ) sin sin sin( ) cos cos cos( ) sin sin sin( ) http://akj9.wordpress.com