the centre of a circle is (2a,a-7) using distance formula find the values of 'a' if the circle passes through - Maths - Coordinate Geometry

Question

the centre of a circle is (2a,a-7) using distance formula find the
values of 'a' if the circle passes through the point (11,-9),and
has the diameter 10 root 2 units

Urvashi Pandoi · Accepted Answer

Dear student,

length of the diameter = $10 \sqrt{2} u n i t s$

therefore the radius r = $\frac{10 \sqrt{2}}{2} = 5 \sqrt{2} u n i t s$

let the center of the circle be C $(2 a, a - 7)$ .

let it passes through the point P(11,-9).

therefore PC= r $\Rightarrow P C^{2} = r^{2}$

$(11 - 2 a)^{2} + (- 9 - a + 7)^{2} = (5 \sqrt{2})^{2} 121 + 4 a^{2} - 44 a + (- a - 2)^{2} = 50 121 + 4 a^{2} - 44 a + a^{2} + 4 + 4 a = 50 5 a^{2} - 40 a + 75 = 0 a^{2} - 8 a + 15 = 0 a^{2} - 3 a - 5 a + 15 = 0 (a - 3) (a - 5) = 0$

therefore a=3 or a=5.

hence the center of the circle is $(2 * 3, 3 - 7) o r (2 * 5, 5 - 7)$

i.e. the center of the circle is (6,-4) or (10,-2).

Regards

the centre of a circle is (2a,a-7) using distance formula find the values of 'a' if the circle passes through the point (11,-9),and has the diameter 10 root 2 units