`A-=(-4,0),B-=(4,0)dotMa n dN` are the variable points of the y-axis such that `M` lies below `Na n dM N=4` . Lines `A Ma n dB N` intersect at `Pdot` The locus of `P` is

If A(-2,1),B(2,3)a n dC(-2,-4) are three points, find the angle between B Aa n dB Cdot

A B is a variable line sliding between the coordinate axes in such a way that A lies on the x-axis and B lies on the y-axis. If P is a variable point on A B such that P A=b ,P b=a , and A B=a+b , find the equation of the locus of Pdot

Let A(6,4)a n dB(2,12) be two given point. Find the slope of a line perpendicular to A Bdot

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O P.O Q=p^2 , then find the locus of the point Qdot

Tangents are drawn to the parabola y^2=4a x at the point where the line l x+m y+n=0 meets this parabola. Find the point of intersection of these tangents.

Let A(−4,0) , B(4,0) & C(x,y) be points on the circle x^2 + y^2 = 16 such that the number of points for which the area of the triangle whose vertices are A, B and C is a positive integer, is N then the value of [N/7] is, where [⋅] represents greatest integer function.

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is

S is a circle having the center at (0,a) and radius b(b < a)dot A variable circle centered at (alpha,0) and touching the circle S meets the X-axis at Ma n dN . Find the a point P on the Y-axis, such that /_M P N is a constant for any choice of alpha

A normal to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 meets the axes at Ma n dN and lines M P and N P are drawn perpendicular to the axes meeting at Pdot Prove that the locus of P is the hyperbola a^2x^2-b^2y^2=(a^2+b^2)dot

Let O be the origin. If A(1,0)a n dB(0,1)a n dP(x , y) are points such that x y >0a n dx+y<1, then P