Circles Test 6...

The equation $$(\mathrm{x}^{2}-\mathrm{a}^{2})^{2}+(\mathrm{y}^{2}-\mathrm{b}^{2})^{2}=0$$ represent points which are

A circle of radius $$5$$ units passes through the points $$(7,1),(9,5)$$. If the ordinate of the centre is less than $$2$$, then the equation of the circle is

The circle $${ S }_{ 1 }$$ with centre $${ C }_{ 1 }\left( { a }_{ 1 },{ b }_{ 1 } \right) $$ and radius $${r}_{1}$$ touches externally the circle $${S}_{2}$$ with centre $${ C }_{ 2 }\left( { a }_{ 2 },{ b }_{ 2 } \right) $$ and radius $${r}_{2}$$. If the tangent at their common point passes through the origin then 

The triangle PQR is inscribed in the circle $$\displaystyle x^{2}+y^{2}= 25.$$ If $$Q$$ and $$R$$ have coordinates $$\displaystyle \left ( 3, 4 \right )$$ and $$\displaystyle \left ( -4, 3 \right ),$$ respectively, then $$\displaystyle \angle QPR$$ is equal to

If chord PQ of a circle have length equal to the radius then  the distance of chord from centre in terms of radius  is

The lines $$\displaystyle 2x - 3y = 5$$ and $$\displaystyle 3x - 4y = 7$$ intersect at the center of the circle whose area is $$154$$ sq. units, then equation of circle is

The equation of circle with origin as a centre and passing through equilateral triangle whose median is of length $$3a$$ is

The equation of the circle passing through the point $$(1, 1)$$ and having two diameters along the pair of lines $$x^{2}-y^{2}-2x+4y-3=0$$ is

The equation of a diameter of a circle is $$x+y=1$$ and the greatest distance of any point of the circle from the diameter is $$\dfrac{1}{\sqrt{2}}$$ .Then, a possible  equation of the circle can be

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