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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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
+
Transcribed Image Text: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 +
Expert Solution
Step 1

The equation of the ellipse is given by

    2x+ y+ 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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