The normal at a point `P` on the ellipse `x^2+4y^2=16` meets the x-axis at `Qdot` If `M` is the midpoint of the line segment `P Q ,` then the locus of `M` intersects the latus rectums of the given ellipse at points. (a)`(+-((3sqrt(5)))/2+-2/7)` (b) `(+-((3sqrt(5)))/2+-(sqrt(19))/7)` (c)`(+-2sqrt(3),+-1/7)` (d) `(+-2sqrt(3)+-(4sqrt(3))/7)`

Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/2 b. (-sqrt(3)+sqrt(-1))/(sqrt(-4)) c. (sqrt(3)-sqrt(-1))/(sqrt(-4)) d. -sqrt(-1)

Length of the latus rectum of the parabola sqrt(x) +sqrt(y) = sqrt(a) is (a) a sqrt(2) (b) (a)/(sqrt(2)) (c) a (d) 2a

If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) meets the auxiliary circle at point R and Q , then find the points of intersection of tangents to the circle at Q and Rdot

If the coordinates of a point lies on the ellipse 9x^2+16y^2=144 be (2,(3sqrt3)/2) ,find the eccentric angle of that point.

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (a) (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

The points on the line x=2 from which the tangents drawn to the circle x^2+y^2=16 are at right angles is (are) (a) (2,2sqrt(7)) (b) (2,2sqrt(5)) (c) (2,-2sqrt(7)) (d) (2,-2sqrt(5))

The coordinates of the point on the ellipse 9x^(2) + 16y^(2) = 144 are (2,(3sqrt(3))/(2)) , find the eccentric angle of the point .

The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. (a)1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) (b)1n((sqrt(3)+sqrt(7))/2) (c)1n((sqrt(7)-sqrt(3))/2) (d)+-1n((sqrt(3)+sqrt(7))/2)

The ellipse x^2/a^2+y^2/b^2=1 passes through the point of intersection of the lines 7x+13y=87and 5x-8y+7=0and the length of its latus rectum is (32sqrt2)/5 units.Find the values of a and b.

A beam of light is sent along the line x-y=1 , which after refracting from the x-axis enters the opposite side by turning through 30^0 towards the normal at the point of incidence on the x-axis. Then the equation of the refracted ray is (a) (2-sqrt(3))x-y=2+sqrt(3) (b) (2+sqrt(3))x-y=2+sqrt(3) (c) (2-sqrt(3))x+y=(2+sqrt(3)) (d) y=(2-sqrt(3))(x-1)