Then angle of intersection of the normal at the point `(-5/(sqrt(2)),3/(sqrt(2)))` of the curves `x^2-y^2=8` and `9x^2+25 y^2=225` is 0 (b) `pi/2` (c) `pi/3` (d) `pi/4`

The angles at which the circles (x-1)^2+y^2=10a n dx^2+(y-2)^2=5 intersect is pi/6 (b) pi/4 (c) pi/3 (d) pi/2

Prove that pi/6 lt int_0^1(dx) /(sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))

The area of the triangle formed by joining the origin to the point of intersection of the line xsqrt(5)+2y=3sqrt(5) and the circle x^2+y^2=10 is (a)3 (b) 4 (c) 5 (d) 6

The angle between the lines joining origin to the points of intersection of the line sqrt(3)x+y=2 and the curve y^2-x^2=4 is (A) tan^(-1)(2/(sqrt(3))) (B) pi/6 (C) tan^(-1)((sqrt(3))/2) (D) pi/2

If the line xcostheta+ysintheta=2 is the equation of a transverse common tangent to the circles x^2+y^2=4 and x^2+y^2-6sqrt(3)x-6y+20=0 , then the value of theta is (a) (5pi)/6 (b) (2pi)/3 (c) pi/3 (d) pi/6

The acute angle between two straight lines passing through the point M(-6,-8) and the points in which the line segment 2x+y+10=0 enclosed between the co-ordinate axes is divided in the ratio 1:2:2 in the direction from the point of its intersection with the x-axis to the point of intersection with the y-axis is: (a) pi/3 (b) pi/4 (c) pi/6 (d) pi/(12)

If the tangent at the point P(theta) to the ellipse 16 x^2+11 y^2=256 is also a tangent to the circle x^2+y^2-2x=15 , then theta= (a) (2pi)/3 (b) (4pi)/3 (c) (5pi)/3 (d) pi/3

The equation of the circle passing through the point of intersection of the circles x^2+y^2-4x-2y=8 and x^2+y^2-2x-4y=8 and the point (-1,4) is (a) x^2+y^2+4x+4y-8=0 (b) x^2+y^2-3x+4y+8=0 (c) x^2+y^2+x+y=0 (d) x^2+y^2-3x-3y-8=0

The angle between the tangents to the parabola y^2=4a x at the points where it intersects with the line x-y-a=0 is (a) pi/3 (b) pi/4 (c) pi (d) pi/2

Find the coordinates of the points of intersection of the curves y=cosx , y=sin3x if-pi/2lt=xlt=pi/2