Tangents `P A` and `P B` are drawn to `x^2+y^2=9` from any arbitrary point `P` on the line `x+y=25` . The locus of the midpoint of chord `A B` is `

Tangents PA and PB are drawn to the circle x^2 +y^2=8 from any arbitrary point P on the line x+y =4 . The locus of mid-point of chord of contact AB is

Tangents are drawn to x^2+y^2=1 from any arbitrary point P on the line 2x+y-4=0 . The corresponding chord of contact passes through a fixed point whose coordinates are (1/2,1/2) (b) (1/2,1) (1/2,1/4) (d) (1,1/2)

Tangents are drawn to x^(2)+y^(2)=1 from any arbitrary point P on the line 2x+y-4=0 .Prove that corresponding chords of contact pass through a fixed point and find that point.

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

Tangents are drawn from any point on the hyperbola (x^2)/9-(y^2)/4=1 to the circle x^2+y^2=9 . Find the locus of the midpoint of the chord of contact.

Tangents PA and PB are drawn to the circle (x-4)^(2)+(y-5)^(2)=4 from the point P on the curve y=sin x , where A and B lie on the circle. Consider the function y= f(x) represented by the locus of the center of the circumcircle of triangle PAB. Then answer the following questions. Which of the following is true ?

If tangents are drawn to y^2=4a x from any point P on the parabola y^2=a(x+b), then show that the normals drawn at their point for contact meet on a fixed line.

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

P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) is another variable point, where c is a constant. The locus of the midpoint of P Q is an (a)parabola (b) ellipse (c)hyperbola (d) circle

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at Aa n dB . The locus of the point of intersection of tangents at Aa n dB to the circle x^2+y^2=9 is x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 y^2-x^2=((27)/7)^2 (d) none of these