Question

For what value of λ dose the line y = x + λ touches the ellipse 9x2 + 16y2 = 144.

Solution

Correct option is

Equation of ellipse is 9x2 + 16y2 = 144

    

Comparing this with         

Then we get a2 = 16 and b2 = 9 and comparing the line y = x + λ with y = mx + c

             m = 1 and c =  λ

If the line y = x + λ touches the ellipse

               9x2 + 16y2 = 144,  then

               c2 = a2m2 + b2

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SIMILAR QUESTIONS

Q1

The equation of the ellipse with focus (–1, 1), directrix x – y + 3 = 0 and eccentricity , is

Q2

The equation of the ellipse whose center is at origin and whihch passes through the points (–3, 1) and (2, –2) is

 

Q3

The equation x2 + 4xy + y2 + 2x + 4y + 2 = 0 represents

Q4

The equation of the tangent to the ellipse x2 + 16y2 = 16 making an angle of 600 with x-axis is

Q5

The equation of the ellipse whose foci are  and one of its directrix is 5x = 36.

Q6

Center of hyperbola 9x2 – 16y2 + 18x + 32y – 151 = 0 is

Q7

The equation of the ellipse whose centre is (2, –3), one of the foci is (3, –3) and the responding vertex is (4, –3) is

Q8

Find the eccentricity of the ellipse, whose foci are (–3, 4) and (3, –4) and which passes through the point (1, 2)

Q9

If  is a tangent to the ellipse , then find out the eccentric angle of the point of tangency.

Q10

Find the equations of the tangents to the ellipse 3x2 + 4y2 = 12 which perpendicular to the line y + 2x = 4.