Question

The equation of the tangent to the ellipse 2x² + 3y² = 30 at the point (- 3, 2) is______.

पर्याय

• y = x + 3

• y = x + 2

• x = y + 5

• y = x + 5

Answer 1

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