If the normals to the curve `y=x^2` at the points `P,Q and R` pas thrugh the points `(0,3/2)`, then find circle circumsecribing the triangle `PQR`.

The equation of the normal to the curve y=x(2-x) at the point (2, 0) is

Find the equation of the normal to the curve ay^(2)=x^(3), at the point (am^(2),am^(3)). If normal passes through the point (a,0) then find the slope.

Tangents PA and PB are drawn to the circle (x+3)^(2)+(y-4)^(2)=1 from a variable point P on y=sin x. Find the locus of the centre of the circle circumscribing triangle PAB.

Tangents PT and QT to the parabola y^2 = 4x intersect at T and the normal drawn at the point P and Q intersect at the point R(9, 6) on the parabola. Find the coordinates of the point T . Show that the equation to the circle circumscribing the quadrilateral PTQR , is (x-2) (x-9) + (y+3) (y-6) = 0 .

If the normal to the parabola y^(2)=12x at the point P(3,6) meets the parabola again at the point Q,then equation of the circle having PQ as a diameter is

The slope of normal to the curve x^(3)=8a^(2)y, a gt 0 at a point in the first quadrant is -(2)/(3) , then point is

If the tangent at the point (p,q) to the curve x^(3)+y^(2)=k meets the curve again at the point (a,b), then

Find the equation of normal to the curve x = at^(2), y=2at at point 't'.