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