Conic Sections ...

Find the length of latus rectum of the parabola whose focus is the point $$\displaystyle \left ( 2,3 \right )$$ and directrix is the line  $$\displaystyle x-4y+3=0.$$ 

On the line joining the points $$A (0,4)$$ and $$B (3, 0)$$, a square $$ABCD $$ is constructed on the side of the line away from the origin. Equation of the circle having centre at $$C$$ and touching the axis of $$x$$ is

The lines $$2x -3y=5$$ and $$3x -4y =7$$ are the diameters of a circle of area $$154$$ square units. An equation of this circle is $$(\pi = 22/7)$$

The equation of circle with origin as center and passing through the vertices of an equilateral triangle whose median is of length $$3a$$ is

If the lines $$2x+3y+1= 0$$ and $$3x-y-4= 0$$ lie along the diameter of a circle of circumference $$10\pi $$, then equation of circle be

Find the latus rectum of the parabola $$x^2\, +\, 2y- 3x\, +\, 5\, =\, 0$$

The lines $$2x-3y=5$$ and $$3x-4y=7$$ are diameters of a circle of area $$154\ sq.\ units$$. The equation of the circle is-

Find the equation of the circle whose centre is the point of intersection of the lines $$2x-3y+4=0$$ and $$3x+4y-5=0$$ and passes through the origin.

The equation of the  circle passing through $$(3,6)$$ and whose centre is $$(2,-1)$$ is-

The equation of the circle drawn with the focus of the parabola $$(x-1)^2 - 8y = 0$$ as its centre and touching the parabola at its vertex is