Question

the center of a circle is (2a, a-7) . find the value of a, if the circle pass through the point (11, -9) and has a diameter 10√2 unit

step by step

please​

Answer 1

Step-by-step explanation:

Centre of the circle (2a, a-7) and passes through (11, -9)

Radius, r = 5√2

Now, equation of circle

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

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

$= > 121 + 4 {a}^{2} - 44a + 4 + {a}^{2} + 4a = 50$

$= > 5 {a}^{2} - 40a + 125 = 50$

$= > 5 {a}^{2} - 40a + 75 = 0$

$= > {a}^{2} - 8a + 15 = 0$

$= > {a}^{2} - 5a - 3a + 15 = 0$

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

$= > a = 5 \: \: or \: \: a = - 3$