Home
Class 11
MATHS
If a and c are positive real number and ...

If a and c are positive real number and the ellipse `x^2/(4c^2)+y^2/c^2=1` has four distinct points in common with the circle `x^2+y^2=9a^2`, then

A

`9ac- 9a^(2)- 2c^(2) lt 0`

B

`6ac + 9a^(2) -2c^(2) lt 0`

C

`9ac - 9a^(2)- 2c^(2) gt 0`

D

`6ac + 9a^(2) -2c^(2) gt 0`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

If a and c are positive real number and ellipse (x^(2))/(4c^(2))+(y^(2))/(c^(2))=1 has four distinct points in comman with the circle x^(2)+y^(2)=9a^(2), then (A) 6ac+9a^(2)-2c^(2)>0(B)6ac+9a^(2)-2c^(2) 0(D)6ac-9a^(2)-2c^(2)<0

If a,b, and c are distinct positive real numbers and a^(2)+b^(2)+c^(2)=1, then ab+bc+ca is

If a, b and c are distinct positive real numbers and a^2 + b^2 + c^2 = 1, then ab + bc + ca is

The circle x^2+y^2=c^2 contains the ellipse x^2/a^2+y^2/b^2=1 if

The line y=2t^2 meets the ellipse (x^2)/(9)+(y^2)/(4)=1 in real points if

The line x=t^(2) meets the ellipse x^(2)+(y^(2))/(9)=1 at real and distinct points if and only if |t| 1( d) none of these

Ifchord ofcontact ofthe tangents drawn from the point (alpha,beta) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the circle x^(2)+y^(2)=c^(2), then the locus of the point

If y=mx+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then the point of contact is

The number of common tangents to the ellipse (x^(2))/(16) + (y^(2))/(9) =1 and the circle x^(2) + y^(2) = 4 is