Question Text
Question 1 :
The equation of the circle which passes through the points $(2, 3)$ and $(4. 5)$ and the centre lies on the straight line $y - 4x + 3 = 0$, is
Question 2 :
The circle $x ^ { 2 } + y ^ { 2 } = 4 x + 8 y + 5$ intersects the line $3 x - 4 y = m$ at two distinct points if :-
Question 3 :
The circle passing through $(t,1)$, $(1,t)$ and $(t,t)$<br/>for all values of $t$ passes through .........<br/>
Question 4 :
lf two conics whose equations refer to rect- angular axes are $\mathrm{a}\mathrm{x}^{2}+2\mathrm{h}\mathrm{x}\mathrm{y}+\mathrm{b}\mathrm{y}^{2}+2\mathrm{g}\mathrm{x}+2\mathrm{f}\mathrm{y}+\mathrm{c}=0$<br>and $\mathrm{a}' \mathrm{x}^{2}+2\mathrm{h}'\mathrm{x}\mathrm{y}+\mathrm{b}' \mathrm{y}^{2}+2\mathrm{g}'\mathrm{x}+2\mathrm{f}\mathrm{y}+\mathrm{c}'=0$ intersect in four concyclic points, then<br>
Question 5 :
The equation of the circle whose centre is $\left(3,\displaystyle \frac{\pi }{4}\right)$ and radius is $5$ is<br/>
Question 6 :
$(a, c)$ and $(b, c)$ are the centres of two circles whose radical axis is the y-axis. If the radius of first circle is $r$ then the diameter of the other circle is