The equation, 2x^2+ 3y^2-8x-18y+35= K re...

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`

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 gt 0`

Text Solution

Verified by Experts

The correct Answer is:

C

Topper's Solved these Questions

CONIC SECTIONS
VMC MODULES ENGLISH|Exercise LEVEL - 2|111 Videos
CONIC SECTIONS
VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|15 Videos
CONIC SECTIONS
VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos
COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos
DIFFERENTIAL CALCULUS
VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

Similar Questions

Explore conceptually related problems

If the equation 2x^(2)+7xy+3y^(2)-9x-7y+k=0 represents a pair of lines, then k is equal to

The equation (x^2)/(1-k)-(y^2)/(1+k)=1, k gt 1 represents:-

If the equation 3x^(2)+xy-y^(2)-3x+6y+k=0 represents a pair of straight lines, then the value of k, is

The equation |z-i|+|z+i|=k, k gt 0 can represent an ellipse, if k=

The equation 3x^2+4y^2-18+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

If the equation 2x^2+k x y+2y^2=0 represents a pair of real and distinct lines, then find the values of k .

The equation (x-alpha)^2+(y-beta)^2=k(l x+m y+n)^2 represents (a) a parabola for k = (l^2+m^2)^(-1) (b) an ellipse for 0 (1^2+m^2)^(-1) (d) a point circle for k=0

The equation |sqrt(x^2+(y-1)^2)-sqrt(x^2+(y+1)^2)|=K will represent a hyperbola for (a) K in (0,2) (b) K in (-2,1) K in (1,oo) (d) K in (0,oo)

If S=0 is the equation of the hyperbola x^2+4x y+3y^2-4x+2y+1=0 , then the value of K for which S+K=0 represents its asymptotes is (a) 20 (b) -16 (c) -22 (d) 18

VMC MODULES ENGLISH-CONIC SECTIONS-LEVEL - 1

tangent drawn to the ellipse x^2/a^2+y^2/b^2=1 at point 'P' meets the ...
Text Solution
|
The eccentricity of ellipse 4(x-2y+1)^2 +9(2x+y+2)^2=180 is
Text Solution
|
The equation, 2x^2+ 3y^2-8x-18y+35= K represents (a) no locus if k g...
Text Solution
|
Consider the ellipse x^(2)/(tan^(2)alpha)+y^(2)/(sec^(2)alpha)=1 where...
Text Solution
|
If alpha and beta are the eccentric angles of the extremities of a f...
Text Solution
|
If the line l x+m y+n=0 cuts the ellipse ((x^2)/(a^2))+((y^2)/(b^2)...
Text Solution
|
The equation of the tangents to the ellipse 4x^(2)+3y^(2)=5, which are...
Text Solution
|
The equation of normal to the ellipse 4x^2 +9y^2 = 72 at point (3,2) i...
Text Solution
|
The locus of the foot of the perpendicular from the foci an any tangen...
Text Solution
|
Show that the tangents drawn at those points of the ellipse (x^(2))/(a...
Text Solution
|
Let the two foci of an ellipse be (-1, 0) and (3, 4) and the foot of p...
Text Solution
|
Let the two foci of an ellipse be (-1,0) and (3,4) and the foot of per...
Text Solution
|
Let the two foci of an ellipse be (-1,0) and (3,4) and the foot of per...
Text Solution
|
Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)...
Text Solution
|
PQ is a double ordinate of the parabola y^(2)=4ax. If the normal at P ...
Text Solution
|
The area of the rectangle formed by the perpendicular from the center ...
Text Solution
|
The length ofthe normal (terminated by the major axis) at a point of t...
Text Solution
|
Find the middle point of the chord intercepted on the line 2x-y+3 =0 b...
Text Solution
|
Find the locus of the mid point of chords of the ellipse x^(2)/a^(2)+y...
Text Solution
|
CP and CD are conjugate semi-diameters of the ellipse x^(2)/a^(2) + y^...
Text Solution
|