# HOW TO FIND EQUATIONS OF TANGENTS DRAWN FROM THE POINT TO THE ELLIPSE

How to Find Equations of Tangents Drawn From the Point to the Ellipse :

Here we are going to see some practice questions to find the equations of tangent drawn from the point to the ellipse.

## How to Find Equations of Tangents Drawn From the Point to the Ellipse - Practice questions

Question 1 :

Find the equations of the two tangents that can be drawn from (5, 2) to the ellipse 2x2 + 7y2 =14 .

Solution :

Equation of tangent drawn to the ellipse will be in the form

y = mx ± √(a2m2 + b2)  ---(1)

(x2/7) + (y2/2) = 1

a =  7, b=  2

The tangent line is passing through the point (5, 2)

2 = m(5) ± √(7m2 + 2)

(2 - 5m)2  =  (7m2 + 2)

4 + 25m2 - 2(2)(5m)  =  7m2 + 2

25m2 7m2  - 20m + 4 - 2  =  0

18m - 20m + 2  =  0

9m- 10m + 1  =  0

(9m - 1) (m - 1)  =  0

m  =  1/9 and m  =  1

 If m = 1/9 a2  =  7 and b2  =  2y = (1/9)x ± √(7(1/9) + 2) y = (1/9)x ± (5/3)9y  =  x  ± 15x - 9y  ± 15  =  0x - 9y + 15  =  0 If m = 1 a2  =  7 and b2  =  2y = x ± √(7(1) + 2) y = x ± 3x - y ± 3 =  0x - y - 3 =  0

Hence the required equation of tangents are x - 9y + 15  =  0 and x - y - 3 =  0.

After having gone through the stuff given above, we hope that the students would have understood, "How to Find Equations of Tangents Drawn From the Point to the Ellipse".

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