Tangents are drawn to `x^2+y^2=16` from the point `P(0, h)dot` These tangents meet the `x-a xi s` at `Aa n dB` . If the area of triangle `P A B` is minimum, then `h=12sqrt(2)` (b) `h=6sqrt(2)` `h=8sqrt(2)` (d) `h=4sqrt(2)`

Tangents P Aa n dP B are drawn to x^2+y^2=a^2 from the point P(x_1, y_1)dot Then find the equation of the circumcircle of triangle P A Bdot

If A(1,p^2),B(0,1) and C(p ,0) are the coordinates of three points, then the value of p for which the area of triangle A B C is the minimum is 1/(sqrt(3)) (b) -1/(sqrt(3)) 1/(sqrt(2)) (d) none of these

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at Aa n dB . Then find the locus of the midpoint of A Bdot

Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) 1-sqrt(2/3) (B) sqrt(3/2) -1 (C) 1+sqrt(2/3) (D) sqrt(3/2)+1

A vertical line passing through the point (h, 0) intersects the ellipse x^2/4+y^2/3=1 at the points P and Q .Let the tangents to the ellipse at P and Q meet at R . If delta (h) Area of triangle deltaPQR , and delta_1 max_(1/2<=h<=1)delta(h) A further delta_2 min_(1/2<=h<=1) delta (h) Then 8/sqrt5 delta_1-8delta_2

Tangents are drawn to the hyperbola x^2/9-y^2/4=1 parallet to the sraight line 2x-y=1. The points of contact of the tangents on the hyperbola are (A) (2/(2sqrt2),1/sqrt2) (B) (-9/(2sqrt2),1/sqrt2) (C) (3sqrt3,-2sqrt2) (D) (-3sqrt3,2sqrt2)

The abscissa of the point on the curve sqrt(x y)=a+x the tangent at which cuts off equal intercepts from the coordinate axes is -a/(sqrt(2)) (b) a//sqrt(2) (c) -asqrt(2) (d) asqrt(2)

The minimum value of (x^4+y^4+z^2)/(x y z) for positive real numbers x ,y ,z is (a) sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) 8sqrt(2)

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/(sqrt(2)) (d) |b|<1/(sqrt(2))

Tangent P Aa n dP B are drawn from the point P on the directrix of the parabola (x-2)^2+(y-3)^2=((5x-12 y+3)^2)/(160) . Find the least radius of the circumcircle of triangle P A Bdot