Eccentricity of hyperbola x^2/a^2-y^2/b^...

Eccentricity of hyperbola `x^2/a^2-y^2/b^2=1` is `sqrt5/2` & length of latus rectum is `sqrt3/2` . If tangent is `y=2x+c` , then value of c is :

`+-(3sqrt5)/2`

`+-(5sqrt3)/2`

`+-(3sqrt2)/5`

`+-(5sqrt2)/3`

Text Solution

AI Generated Solution

Topper's Solved these Questions

JEE MAIN 2021
JEE MAINS PREVIOUS YEAR|Exercise Mathematic section B|10 Videos
JEE MAIN 2023
JEE MAINS PREVIOUS YEAR|Exercise Question|435 Videos

Similar Questions

Explore conceptually related problems

Eccentricity of a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is " (sqrt(41))/(5), the ratio of length of transverse axis to the conjugate axis is

The length of the latus rectum of 3x^(2) - 2y^(2) =6 is

The line 2y=3x+12 cuts the parabola 4y=3x^(2) . The hyperbola x^(2)/a^(2)+y^(2)/b^(2)=1 passes through the point (3sqrt5,1) and the length of its latus rectum is 4/3 units. The length of the conjugate axis is

let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal to that of the ellipse x^2+4y^2=4. if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is x^2/3-y^2/2=1 (b) a focus of the hyperbola is (2,0) (c) the eccentricity of the hyperbola is sqrt(5/3) (d) the equation of the hyperbola is x^2-3y^2=3

The normla to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 drawn at an extremity of its latus rectum is parallel to an asymptote. Show that the eccentricity is equal to the square root of (1+sqrt(5))//2.

The eccentricity of the hyperbola (sqrt(1999))/(3)(x^(2)-y^(2))=1 , is

If the eccentricity of the ellipse,(x^(2))/(a^(2)+1)+(y^(2))/(a^(2)+2)=1 is (1)/(sqrt(6)) then latus rectum of ellipse is

The eccentricity of the hyperbola (sqrt(2006))/(4) (x^(2) - y^(2))= 1 is

JEE MAINS PREVIOUS YEAR-JEE MAIN 2022-Question

How many 5 digit multiples of 6 can be formed using digit {1,2,3,5,6,7...
Text Solution
|
Two poles AB , PQ are 160m apart and C is the mid-point of BQ on the g...
Text Solution
|
Eccentricity of hyperbola x^2/a^2-y^2/b^2=1 is sqrt5/2 & length of lat...
Text Solution
|
sum(k=1)^31 .^31Ck.^31C(k-1) - sum(k=1) ^30 .^30Ck.^30C(k-1) is equal ...
Text Solution
|
Consider the circle x^2+y^2-2x-4y=0. If O represents origin , point P ...
Text Solution
|
Find acute angle between two planes P1 and P2 passing through the inte...
Text Solution
|
veca=2hati+hatj+3hatk , vecb=3hati+3hatj+hatk & vecc=c1hati+c2hatk+c3h...
Text Solution
|
x((x)/(sqrt(x^2-y^2))+e^(y/x))dy/dx=y(x/(sqrt(x^2-y^2))+e^(y/x))+x Let...
Text Solution
|
If in a given GP series a1 xx a3 xx a5 xx a7 = 1/1296 ,and a2+a4=7/36 ...
Text Solution
|
If int0^1 [-8x^2+6x+1]dx=t where [.] denotes G.I.F then t equals to
Text Solution
|
Let f:NN to NN be defined as f(x)={(2n,if n=2,4,6 . . .),(n-1,if n=3,...
Text Solution
|
S1 : p to (e vv q) S2 : (~p vv q) vv (~p vv e) Which of the followi...
Text Solution
|
The term independent of x in (2x^3+3/x^k)^12 is equal to 2^8 l , where...
Text Solution
|
If relation defined on set A= {1,2,3, . . .,50} , and relation R1 {(p,...
Text Solution
|
6 tan(lim(n to oo) sum(r=1)^n tan^-1(1/(r^2+3r+3)))=
Text Solution
|
The coefficient of the term independent of x in (1-x^2+3x^3)(5/2x^3-1...
Text Solution
|
Find the area enclosed by x-axis & y=3-abs(x+1)-abs(x-1/2)
Text Solution
|
If vertex of parabola is (2,-1) and equation of its directrix is 4x-3y...
Text Solution
|
If cot alpha = -1 , sec beta=-5/3 , where alpha in (pi/2,pi) and beta ...
Text Solution
|
30 identical candies are distributed among 4 students S1,S2,S3 and S4....
Text Solution
|