Question

The equation of the ellipse with its centre at (1, 2), one focus at (6, 2) and passing through the point (4, 6) is ______.

Options

• `(x - 1)^2/45 + (y - 2)^2/20` = 1

• `(x - 1)^2/35 + (y - 2)^2/20` = 1

• `(x - 1)^2/45 + (y - 2)^2/25` = 1

• `(x - 1)^2/50 + (x - 2)^2/25` = 1

Answer 1

The equation of the ellipse with its centre at (1, 2), one focus at (6, 2) and passing through the point (4, 6) is `underlinebb((x - 1)^2/45 + (y - 2)^2/20 = 1)`.

Explanation:

Centre (1, 2), focus A(6, 2) another focus B(–4, 2). If P(4, 6)

⇒ 2a = AP + BP

⇒ 4a² = `(sqrt(2^2 + 4^2) + sqrt(8^2 + 4^2))^2` = 36.5

⇒ a² = 45

⇒ b² = 20