Question

Length of $y-$ intercept made by the circle $5x^2+5y^2-2x+6y-8=0$ is:

• A. $\frac{19}{5}$
• B. $\frac{14}{5}$
• C. $\frac{11}{5}$
• D. $\frac{9}{5}$

Answer 1

The correct option is B $\frac{14}{5}$

Equation of circle:-

$5x^2+5y^2-2x+6y-8=0$

We know that, the general equation of circle is

$x^2+y^2+2yx+2fy+c$

& length of $y-intercept=2\sqrt{f^2-c}$

Here $x^2+y^2-\frac{2}{5}x+2\times \frac{3}{5}y-\frac{8}{5}=0$

So, $f=\frac{3}{5};c=\frac{-8}{5}$

Length $=2\sqrt{\frac{9}{25}+\frac{8}{5}}=2\sqrt{\frac{49}{25}}$

$=2\times \frac{7}{5}=\frac{14}{5}$