The two points `A` and `B` in a plane are such that for all points `P` lies on circle satisfied `PA/PB=k` , then `k` will not be equal to

Statement 1: let A( vec i+ vec j+ vec k)a n dB( vec i- vec j+ vec k) be two points. Then point P(2 vec i+3 vec j+ vec k) lies exterior to the sphere with A B as its diameter. Statement 2: If Aa n dB are any two points and P is a point in space such that vec P Adot vec P B >0 , then point P lies exterior to the sphere with A B as its diameter.

The coordinates of the point Aa n dB are (a,0) and (-a ,0), respectively. If a point P moves so that P A^2-P B^2=2k^2, when k is constant, then find the equation to the locus of the point Pdot

If A(-6,-6) and B(-6,4) be two points that a point P on the line AB satisfies AP=2//9AB . find the point P

Two tangents PA and PB are drawn from an external point P to a circle with centre at O. If AOB = 105^(@) the A hat(P) B is :

In the figure ,PA and PB are tangents to the circle drawn from an external point P. also CD is a tangent to the circle at Q. if PA = 8 cm and CQ = 3cm , then PC is equal to …………..

A(-2, 0) and B(2,0) are two fixed points and P 1s a point such that PA-PB = 2 Let S be the circle x^2 + y^2 = r^2 , then match the following. If r=2 , then the number of points P satisfying PA-PB = 2 and lying on x^2 +y^2=r^2 is

Perpendiculars are drawn, respectively, from the points Pa n dQ to the chords of contact of the points Qa n dP with respect to a circle. Prove that the ratio of the lengths of perpendiculars is equal to the ratio of the distances of the points Pa n dQ from the center of the circles.

Draw a tangent to a circle of radius 3 cm and centre O at any point K on the circle.

Let P(a sectheta, btantheta) and Q(aseccphi , btanphi) (where theta+phi=pi/2 be two points on the hyperbola x^2/a^2-y^2/b^2=1 If (h, k) is the point of intersection of the normals at P and Q then k is equal to (A) (a^2+b^2)/a (B) -((a^2+b^2)/a) (C) (a^2+b^2)/b (D) -((a^2+b^2)/b)