The circle passing through the point (–1, 0) and touching the y‑axis at (0, 2) also passes through the point

Engineering

Mathematics

Intercept from a Circle

Question

(–4, 0)

$(\frac{- 3}{2}, 0)$

$(\frac{- 3}{2}, \frac{5}{2})$

$(\frac{- 5}{2}, 2)$

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$∴$ (h – 0)² + (2 – 2)² = (h + 1)² + (2 – 0)²

h² = h² + 1 + 2h +4

$h = - \frac{5}{2}$

Equation of circle is

${(x + \frac{5}{2})}^{2} + {(y - 2)}^{2} = {(- \frac{5}{2} - 0)}^{2}$

$x^{2} + \frac{25}{4} + 5 x + y^{2} + 4 - 4 y = \frac{25}{4}$

x² +y² + 5x – 4y + 4 = 0

from given points only point (–4, 0) satisfies this equation.

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