Let `P` be the family of parabolas `y=x^2+p x+q ,(q!=0),` whose graphs cut the axes at three points. The family of circles through these three points have a common point

Find the differential equation of the family of circles passing through the points (a,0) and (-a,0)

Draw three circles passing through the points P and Q, where PQ=4 cm

Suppose a parabola y = x^(2) - ax-1 intersects the coordinate axes at three points A,B and C, respectively. The circumcircle of DeltaABC intersects the y-axis again at the point D(0,t) . Then the value of t is

P, Q, and R are the feet of the normals drawn to a parabola ( y−3)^2=8(x−2) . A circle cuts the above parabola at points P, Q, R, and S. Then this circle always passes through the point. (a)(2, 3)(b)(3, 2)(c)(0, 3) (d) (2, 0 )

The tangent at any point P onthe parabola y^2=4a x intersects the y-axis at Qdot Then tangent to the circumcircle of triangle P Q S(S is the focus) at Q is

Consider the family of all circles whose centers lie on the straight line y=x . If this family of circles is represented by the differential equation P y^(primeprime)+Q y^(prime)+1=0, where P ,Q are functions of x , y and y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)), then which of the following statements is (are) true? (a) P=y+x (b) P=y-x (c) P+Q=1-x+y+y^(prime)+(y^(prime))^2 (d) P-Q=x+y-y^(prime)-(y^(prime))^2

If focal distance of a point P on the parabola y^(2)=4ax whose abscissa is 5 10, then find the value of a.

The parabola y=x^2+p x+q cuts the straight line y=2x-3 at a point with abscissa 1. Then the value of pa n dq for which the distance between the vertex of the parabola and the x-axis is the minimum is p=-1,q=-1 (b) p=-2,q=0 p=0,q=-2 (d) p=3/2,q=-1/2

If the chord of contact of tangents from a point P to a given circle passes through Q , then the circle on P Q as diameter.