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Question
The equation of the tangent to the ellipse 2x² + 3y² = 30 at the point (- 3, 2) is______.
Options
y = x + 3
y = x + 2
x = y + 5
y = x + 5
MCQ
Fill in the Blanks
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Solution
The equation of the tangent to the ellipse 2x² + 3y² = 30 at the point (- 3, 2) is y = x + 5.
Explanation:
Ellipse: \[2x^2+3y^2=30,\] Point: (-3, 2)
The equation of the tangent to \[2x^2+3y^2=30,\] at point \[(x_1,y_1)\] is:
\[2x\cdot x_1+3y\cdot y_1=30\]
Substituting \[(x_1,y_1)\] = (-3, 2) :
2x (-3) + 3y(2) = 30
- 6x + 6y = 30
- x + y = 5
y = x + 5
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