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the line x+y=1 intersects the ellipse at 4x 2 +y 2 =4 at the points p and q.find the coordinates of p and q.also find length of chord pq.

the line x+y=1 intersects the ellipse at 4x2+y2=4 at the points p and q.find the coordinates of p and q.also find length of chord pq.

Grade:11

1 Answers

Shiv
13 Points
7 years ago
x+y=1 => y=1-x On putting valu of y in the equation of ellipse,4x^2 + (1-x)^2 = 4 Solving this , we get x=1 or -3/5 Put value of `x` in the equation of Ellipse , we get y=0 or 8/5Therefore, P(1,0) & Q(-3/5 , 8/5) Now, find the distance through formula "[(x1-x2)^2 + (y1-y2)^2]^1/2"

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