SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE Through the point P(-2,-7) tangents are drawn to the ellipse 2x² + y² + 2x-3y - 2 = 0; determine the equations of the tangents and the points of tangency +
SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE Through the point P(-2,-7) tangents are drawn to the ellipse 2x² + y² + 2x-3y - 2 = 0; determine the equations of the tangents and the points of tangency +
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Step 1
The equation of the ellipse is given by
2x2 + y2 + 2x - 3y - 2 = 0 . . . . . . . (1)
Let, the point of tangency be (x, y).
Now, differentiating (1) w.r.t x, we get,
4x + 2y(dy/dx) + 2 - 3(dy/dx) = 0
=> dy/dx = (4x + 2)/(3 - 2y)
– This is the slope of the tangent at (x, y).
Again the tangent line passes through (x, y) and (-2, -7).
So, slope of the tangent = (y + 7)/(x + 2)
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