Question

The equation of the circle whose diameter lies on 2x + 3y = 3 and 16x - y = 4 which passes through (4,6) is

• A. $5(x^2+y^2)-3x-8y=200$
• B. $x^2+y^2-4x-8y=200$
• C. $5(x^2+y^2)-4x=200$
• D. $x^2+y^2=40$

Answer 1

The correct option is A $5(x^2+y^2)-3x-8y=200$

Let point $(x_1,y_1)$ on the diameter.

$\Rightarrow 2x_1+3y_1=3$ ….(i)

$16x_1-y_1=4$ ….(ii)

On solving (i) and (ii), we get centre,

$\Rightarrow x_1=\frac{3}{10},y_1=\frac{4}{5}$
$\because$ Equation of circle,

$(x-x_1{)}^2+(y-y_1{)}^2=r^2\Rightarrow {(x-\frac{3}{10})}^2+{(y-\frac{4}{5})}^2=r^2$

$\because$ Circle passes through (4, 6).

So, $r^2={\left(\frac{37}{10}\right)}^2+{\left(\frac{26}{5}\right)}^2\Rightarrow r^2=\frac{4073}{100}$

$\because$ Required equation of circle is

${(x-\frac{3}{10})}^2+{(y-\frac{4}{5})}^2=\frac{4073}{100}$

$\Rightarrow 5(x^2+y^2)-3x-8y=200.$