Home
Class 12
MATHS
The equation 3x^2+4y^2-18+16 y+43=k rep...

The equation `3x^2+4y^2-18+16 y+43=k` represents an empty set, if `k<0` represents an ellipse, if `k >0` represents a point, if `k=0` cannot represent a real pair of straight lines for any value of `k`

A

represent an empty set, if `klt0`

B

represent an ellipse if `kgt0`

C

represent a poin, if k=0

D

cannot repreent a real paor of straight lines for any value of k

Text Solution

Verified by Experts

`(sqrt(3)x-3sqrt(3))^(2)+(2y+4)^(2)=k`
So, no locus for `klt0`, ellipse for `kgt0`, and point k =0 ,
Promotional Banner

Similar Questions

Explore conceptually related problems

The equation 3x^2+4y^2-18x+16 y+43=k represents an empty set, if k 0 represents a point, if k=0 cannot represent a real pair of straight lines for any value of k

The second degree equation x^2+4y^2-2x-4y+2=0 represents

x^2-x y+y^2-4x-4y+16=0 represents a. a point b. a circle c. a pair of straight line d. none of these

If x^2-3xy+lambda y^2+3x-5y+2=0 ,represent a pair of straight lines, then the value of lambda is

Show that the equation 9x^2-16 y^2-18 x+32 y-151=0 represents a hyperbola.

If k x^2 + 10 xy + 3 y^2 - 15x - 21y + 18 = 0 represents a pair of straight lines. Then the value of k is :

The equation, 2x^2+ 3y^2-8x-18y+35= K represents (a) no locus if k gt 0 (b) an ellipse if k lt 0 (c) a point if k = 0 (d) a hyperbola if k gt0

The equation y^(2) + 4x + 4y + k = 0 represents a parabola whose latus rectum is _

The equation (x-alpha)^2+(y-beta)^2=k(l x+m y+n)^2 represents

The equation x^2y^2-9y^2-6x^2y+54 y=0 represents (a) a pair of straight lines and a circle (b) a pair of straight lines and a parabola (c) a set of four straight lines forming a square (d) none of these