Question

The line 2x + 3y = 12 touches the ellipse `x^2/9 + y^2/4` = 2 at the point (3, 2).

Options

• True

• False

Answer 1

This statement is True.

Explanation:

If line 2x + 3y = 12 touches the ellipse `x^2/9 + y^2/4` = 2

Then the point (3, 2) satisfies both line and ellipse.

∴ For line 2x + 3y = 12

2(3) + 3(2) = 12

6 + 6 = 12

12 = 12

For ellipse `x^2/9 + y^2/4` = 2

`(3)^2/9 + (2)^2/4` = 2

`9/9 + 4/4` = 2

1 + 1 = 2

2 = 2