If two different tangents of `y^2=4x` are the normals to `x^2=4b y ,` then (a)`|b|>1/(2sqrt(2))` (b) `|b|<1/(2sqrt(2))` (c)`|b|>1/(sqrt(2))` (d) `|b|<1/(sqrt(2))`

If the tangent to the curve y^(2)=ax^(2)+b at the point (2,3) is y=4x-5, then (a,b)=

In a triangle A B C , a line X Y is drawn parallel to B C meeting A B in X and A C in Y . The area of the triangle A X Y is half of the area of the triangle A B C . X Y divides A B in the ratio of 1 :sqrt(2) (b) sqrt(2) :(sqrt(2)-1) (c) 1 :(sqrt(2)-1) (d) sqrt(2) :sqrt(3)

If x=5+2sqrt(6), then sqrt((x)/(2))-(1)/(sqrt(2x))= (a) 1 (b) 2 (c) 3 (d) 4

Find the equations of the tangent and the normal to the curve (x^2)/(a^2)-(y^2)/(b^2)=1 at (sqrt(2)a ,\ b) at indicated points.

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

If the area of the triangle formed by the lines x=0,y=0,3x+4y-a(a>0) is 1, then a=(A)sqrt(6)(B)2sqrt(6)(C)4sqrt(6)(D)6sqrt(2)

The radius of a circle,having minimum area, which touches the curve y=4-x^(2) and the lines,y=|x| is: (a) 4(sqrt(2)+1)( b) 2(sqrt(2)+1) (c) 2(sqrt(2)-1)( d) 4(sqrt(2)-1)

Tangents are drawn to x^2+y^2=16 from P(0,h). These tangents meet x-axis at A and B.If the area of PAB is minimum, then value of h is: (a) 12sqrt2 (b) 8sqrt2 (c) 4sqrt2 (d) sqrt2

Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), and the circle x^2+y^2=a^2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan^(-1)((a-b)/(2sqrt(a b))) (B) tan^(-1)((a+b)/(2sqrt(a b))) (C) tan^(-1)((2a b)/(sqrt(a-b))) (D) tan^(-1)((2a b)/(sqrt(a+b)))

The line y=mx+1 is a tangent to the curve y^2=4x if the value of m is (A) 1 (B) 2 (C) 3 (D) 1/2 .