Conic Sections ...

The intercept on the line $$y=x$$ by the circle $${ x }^{ 2 }+{ y }^{ 2 }-2x=0$$ is $$AB$$. Equation of the circle with $$AB$$ as a diameter is

The equation $$\displaystyle \frac {x^2}{8-t}\, +\, \displaystyle \frac {y^2}{t-4}\, =\, 1$$ will represent an ellipse if

The normal at the point $$(3, 4)$$ on a circle cuts the circle again at the point $$(1, 2)$$. Then the equation of the circle is -

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

For the points on the circle $$\displaystyle x^{2}+y^{2}-2x-2y+1=0$$, the sum of maximum and minimum values of $$4x + 3y$$ is 

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

The centre of a circle is $$( x -2 , x+1 )$$ and it passes through the points $$( 4 , 4 )$$ Find the value ( or values ) of $$x$$, if the diameter of the circle is of length $$\displaystyle 2\sqrt{5}$$ units. 

The equation circle whose center is $$(0,0)$$ and radius is $$4$$ is 

Two circles touch each other externally at C and a common tangent touches them at A and B. Which one is true?

Find the center-radius form of the equation of the circle with center $$\left( 4,0 \right) $$ and radius $$7$$