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 +

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)