Question

the centre of a circle is (2a,a-7). find the value of a, if the circle passes through the pt. (11,-9) and has diameter 10underoot2 units

Answer 1

this is Ur required result

Answer 2

Answer:

The value of a is either 3 or 5.

Step-by-step explanation:

The center of the circle is (2a,a-7) and the diameter is $10\sqrt{2}$.

The radius of the circle is

$r=\frac{d}{2}=\frac{10\sqrt{2}}{2}=5\sqrt{2}$

The general form of a circle is

$(x-h)^2+(y-k)^2=r^2$

Where, (h,k) is center and r is radius.

The equation of given circle is

$(x-2a)^2+(y-a+7)^2=(5\sqrt{2})^2$

$(x-2a)^2+(y-a+7)^2=50$                       ....(1)

The circle passing through the point (11,-9).

$(11-2a)^2+(-9-a+7)^2=50$

$121-44a+4a^2+a^2+4a+4=50$

$5a^2-40a+75=0$

Divide by 5.

$a^2-8a+15=0$

$a^2-5a-3a+15=0$

$a(a-5)-3(a-5)=0$

$(a-5)(a-3)=0$

$a=3,5$

Therefore the value of a is either 3 or 5.