Tiêu đề 9. CHAPTER.pdf ✅

(b.) Statement-I is true; statement-II is true; statement-II is not a correct explanation for statement-1 (c.) Statement-I is true; statement-II is false (d.) Statement-I is false; statement-II, is true (7.) The locus of the foot of perpendicular drawn from the centre of the ellipse 2 2 x y + = 3 6 on any tangent to it is [JEE (Main)-2014] (a.) ( ) 2 2 2 2 2 x y x y + = + 6 2 (b.) ( ) 2 2 2 2 2 x y x y + = − 6 2 (c.) ( ) 2 2 2 2 2 x y x y − = + 6 2 (d.) ( ) 2 2 2 2 2 x y x y − = − 6 2 (8.) The slope of the line touching both the parabolas 2 y x = 4 and 2 x y = −32 is [JEE (Main)-2014] (a.) 1 8 (b.) 2 3 (c.) 1 2 (d.) 3 2 (9.) The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse 2 2 1 9 5 + = x y , is [JEE (Main)-2015] (a.) 27 4 (b.) 18 (c.) 27 2 (d.) 27 (10.) Let O be the vertex and Q be any point on the parabola, 2 x y = 8 . If the point P divides the line segment OQ internally in the ratio 1:3 , then the locus of P is [JEE (Main)-2015] (a.) 2 x y = (b.) 2 y x = (c.) 2 y x = 2 (d.) 2 x y = 2 (11.) Let P be the point on the parabola, 2 y x = 8 which is at a minimum distance from the centre C of the circle, 2 2 x y + + = ( 6) 1 . Then the equation of the circle, passing through C and having its centre at P is [JEE (Main)-2016] (a.) 2 2 x y x y + − + − = 4 12 0 (b.) 2 2 2 24 0 4 + − + − = x x y y (c.) 2 2 x y x y + − + + = 4 9 18 0 (d.) 2 2 x y x y + − + + = 4 8 12 0 (12.) The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is [JEE (Main)-2016] (a.) 4 3 (b.) 2 3 (c.) 3 (d.) 4 3

(20.) Let A(4, 4− ) and B(9,6) be points on the parabola, 2 y x = 4 . Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of ACB is maximum. Then, the area (in sq. units) of ACB , is [JEE (Main)-2019] (a.) 32 (b.) 3 31 4 (c.) 1 31 4 (d.) 1 30 2 (21.) A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x -axis. Then the eccentricity of the hyperbola is [JEE (Main)-2019] (a.) 3 2 (b.) 3 (c.) 2 3 (d.) 2 (22.) If the parabolas ( ) 2 y b x c = − 4 and 2 y ax = 8 have a common normal, then which one of the following is a valid choice for the ordered triad (abc , , ) ? [JEE (Main)- 2019] (a.) 1 , 2,0 2       (b.) 1 , 2,3 2       (c.) (1,1,0) (d.) (1,1,3) (23.) The equation of a tangent to the hyperbola 2 2 4 5 20 x y − = parallel to the line x y − = 2 is [JEE (Main)-2019] (a.) x y −+= 7 0 (b.) x y − + =1 0 (c.) x y − − =3 0 (d.) x y − + =9 0 (24.) The length of the chord of the parabola 2 x y = 4 having equation x y − + = 2 4 2 0 is [JEE (Main)-2019] (a.) 3 2 (b.) 6 3 (c.) 2 11 (d.) 8 2 (25.) Let ( ) 2 2 2 , : 1 1 1   =  − =     + − y x S x y R r r , where r 1 . Then S represents [JEE (Main)-2019] (a.) An ellipse whose eccentricity is 1 , when 1. 1  + r r (b.) An ellipse whose eccentricity is 2 , when 1. 1  + r r (c.) A hyperbola whose eccentricity is 2 , 0 1 1 when r r   + (d.) A hyperbola whose eccentricity is