Find the area of circle `4x^2+4y^2=9` which is interior to the parabola `x^2=4y`

Find the equation of line which is normal to the parabola x^(2)=4y and touches the parabola y^(2)=12x .

The largest value of a for which the circle x^2+y^2=a^2 falls totally in the interior of the parabola y^2=4(x+4) is 4sqrt(3) (b) 4 (c) 4(sqrt(6))/7 (d) 2sqrt(3)

Find the area of the region which is inside the parabola y = - x^(2) + 6x - 5 , outside the parabola y = - x^(2) + 4x - 3 and left of the straight line y = 3x-15 .

Find the equation of the circle which is concentric with the circle x^2 +y^2 - 4x+6y-3=0 and the double of its area.

Find the radius of the largest circle, which passes through the focus of the parabola y^2=4(x+y) and is also contained in it.

If the circle x^(2)+y^(2)+2ax=0, a in R touches the parabola y^(2)=4x , them

Find the equation of the circle which cuts each of the circles x^2+y^2=4 , x^2 +y^2-6x-8y.+ 10=0 & x^2 + y^2+2x-4y-2 = 0 at the extremities of a diameter

Find the locus of the middle points of the chords of the parabola y^(2) = 4x which touch the parabola x^(2) = -8y .

If (-2a,a+1) lies in the interior (smaller region) bounded by the circle x^2+y^2=4 and the parabola y^2=4ax , then find the values of a

If (-2a,a+1) lies in the interior (smaller region) bounded by the circle x^2+y^2=4 and the parabola y^2=4x , then