If the curves (x^(2))/(a^(2))-(y^(2))/(b...

If the curves `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1 (agtb) and x^(2)-y(2)=c^(2)` cut at right angle then

`a^2+b^2=2c^2`

`b^2-a^2=2c^2`

`a^2-b^2=2c^2`

None of these

Text Solution

Verified by Experts

The correct Answer is:

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 x^2/a^2+y^2/b^2=1(a>b) and x^2-y^2=c^2 cut at right angles, then:

If the curves (x^(2))/(a^(2))+(y^(2))/(4)=1 and y^(3)=16x intersect at right angles , then 3a^(2) is equal to ________

If the curves (x ^(2))/(a ^(2))+ (y^(2))/(4)= 1 and y ^(2)= 16x intersect at right angles, then:

If the curves (x ^(2))/(a ^(2))+ (y^(2))/(4)= 1 and y ^(3)= 16x intersect at right angles, then:

If the curves (x^2)/(a^2)+(y^2)/(b^2)=1 and (x^2)/(l^2)-(y^2)/(m^2)=1 cut each other orthogonally then.....

If the curves (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 intersect orthogonally, then

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the value of (1)/(y_(1))+(1)/(y_(2)) is

If the ellipse x^2/a^2+y^2/b^2=1 (b > a) and the parabola y^2 = 4ax cut at right angles, then eccentricity of the ellipse is (a) (3)/(5) (b) (2)/(3) (c) (1)/(sqrt(2)) (d) (1)/(2)

The line y=x+rho (p is parameter) cuts the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at P and Q, then prove that mid point of PQ lies on a^(2)y=-b^(2)x .

Show that the tangents drawn at those points of the ellipse (x^(2))/(a)+(y^(2))/(b)=(a+b) , where it is cut by any tangent to (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , intersect at right angles.

VMC MODULES ENGLISH-CONIC SECTIONS-LEVEL - 1

The product of perpendicular drawn from any points on a hyperbola (x^2...
Text Solution
|
The locus of the point of intersection of the tangents at the ends of ...
Text Solution
|
If the curves (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 (agtb) and x^(2)-y(2)=...
Text Solution
|
A normal to the hyperbola (x^2)/4-(y^2)/1=1 has equal intercepts on th...
Text Solution
|
Which of the following equations in parametric form can represent a hy...
Text Solution
|
The distance of the origin from the normal drawn at the point (1,-1) o...
Text Solution
|
Tangent is drawn at the point (-1,1) on the hyperbola 3x^2-4y^2+1=0. T...
Text Solution
|
Let LL1 be a latusrectum of a hyperbola and S1 is the other focus. If ...
Text Solution
|
If a latus rectum of an ellipse subtends a right angle at the centre o...
Text Solution
|
I the latus rectum through one focus of a hyperbola subtends a right ...
Text Solution
|
The transverse axis of the hyperbola 5x^2-4y^2-30x-8y+121=0 is
Text Solution
|
If the pair of lines b^2x^2-a^2y^2=0 are inclined at an angle theta, t...
Text Solution
|
If 2^a+2^(4-a) lt 17, then (x^2)/(a)+(y^2)/(b)=1 reperesents
Text Solution
|
If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2...
Text Solution
|
If the tangents drawn from a point on the hyperbola x^2-y^2=a^2-b^2 to...
Text Solution
|
The locus of a point from which two tangent are drawn to x^2-y^2=a^2 w...
Text Solution
|
Let a and b be bonzero real numbers. Then the equation (ax^(2)+by^(2)+...
Text Solution
|
If e1 is the eccentricity of the ellipse x^2/16+y^2/25=1 and e2 is th...
Text Solution
|
about to only mathematics
Text Solution
|
Let a1" and "b1 be intercepts made by the tangent at point P on xy=c^2...
Text Solution
|