Question

Find a if the distance between (a, 2) and (3, 4) is 8.

Answer 1

Answer:

correct answer is 3+2√15 or 3-2√15

Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

We know that,

$\Large{\implies{\boxed{\boxed{\sf{Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}}}}}$

Where,

• x1 = a
• x2 = 3
• y1 = 2
• y2 = 4

_______________[Put Values]

$\sf{→ 8 = \sqrt{(3 - a)^2 + (4 - 2)^2}} \\ \\ \Large{\implies{\boxed{\boxed{\sf{(a - b)^2 = a^2 + b^2 - 2ab}}}}} \\ \\ \sf{→ 8 = \sqrt{(3)^2 + a^2 - 2(a)(3) + (2)^2}} \\ \\ \sf{→ 8 = \sqrt{9 + a^2 - 6a + 4}} \\ \\ \sf{→ 8^2 = 13 + a^2 - 6a} \\ \\ \sf{→ a^2 - 6a + 13 - 64 = 0} \\ \\ \sf{→ a^2 - 6a + 51 = 0}$

$\rule{150}{2}$

Now,

$\Large{\implies{\boxed{\boxed{\sf{a = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}}}}}$

$\sf{→ a = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(51)}}{2(1)}} \\ \\ \sf{→ a = \frac{6 \pm \sqrt{36 - 204}}{2}} \\ \\ \sf{→ a = \frac{6 \pm \sqrt{204}}{2}}$