Home
Class 12
MATHS
If the ellipse (x^2)/4+y^2=1 meets the e...

If the ellipse `(x^2)/4+y^2=1` meets the ellipse `x^2+(y^2)/(a^2)=1` at four distinct points and `a=b^2-5b+7,` then `b` does not lie in `[4,5]` (b) `(-oo,2)uu(3,oo)` `(-oo,0)` (d) `[2,3]`

A

[4,5]

B

`(-oo,2)uu(3,oo)`

C

`(-oo,0)`

D

[2,3]

Text Solution

Verified by Experts

For the two ellipse to intersect a four distinct point `agt1`
`:. b^(2)-5b+7gt`
`or b^(2)-5b+6gt0`
or `b in (-oo,2)uu(3,oo)`
Therefore, b does not lie in [2,3]
Promotional Banner

Similar Questions

Explore conceptually related problems

The line x = at^(2) meets the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 in the real points iff

The line x+2y=1 cuts the ellipse x^(2)+4y^(2)=1 1 at two distinct points A and B. Point C is on the ellipse such that area of triangle ABC is maximum, then find point C.

If a point (a,2) lies between the lines x-y-1=0 and 2(x-y)-5=0 , then the set of values of a is (A) (-oo,3)uu(9/2,oo) (B) (3,9/2) (C) (-oo,3) (D) (9/2,oo)

If the root of the equation (a-1)(x^2-x+1)^2=(a+1)(x^4+x^2+1) are real and distinct, then the value of a in a. (-oo,3] b. (-oo,-2)uu(2,oo) c. [-2,2] d. [-3,oo)

If 3 - 2x^(2) gt 5x, x in R , then the set of solutions is A. (- oo,-1/2) B. (3,oo) C. (-1/2,3) D. [-1/2,3]

If |x-1|>5, then a. x in (-4,6) b. x in [-4,6] c. x in (-oo,-4)uu(6,oo) d. x in (-oo,-4)uu[6,oo)

The equation ||x-2|+a|=4 can have four distinct real solutions for x if a belongs to the interval (-oo,-4) (b) (-oo,0) (4,oo) (d) none of these

The equation ||x-2|+a|=4 can have four distinct real solutions for x if a belongs to the interval a) (-oo,-4) (b) (-oo,0) c) (4,oo) (d) none of these

f(x)=(x-2)|x-3| is monotonically increasing in (a) (-oo,5/2)uu(3,oo) (b) (5/2,oo) (c) (2,oo) (d) (-oo,3)

If the point (2,k) lies outside the circles x^2+y^2+x-2y-14=0a n dx^2+y^2=13" then k" lies in the interval (a) (-3,-2)uu(3,4) (b) (-3,4) (c) (-oo,-3)uu(4,oo) (d) (-oo-2)uu(3,oo)