[16x^(2)-9y^(2)=144],[9x^(2)-16y^(2)=144],[25x^(2)-9y^(2)=225],[9x^(2)-25y^(2)=81]

Equation of het hyperbola whose vertices are (+-3,0) and foci at (+-5,0) is 16x^(2)-9y^(2)=144 b.9x^(2)-16y^(2)=144c25x^(2)-9y^(2)=225d.9x^(2)-25y^(2)=81

Equation of the hyperbola whose vertices are (+-3,0) and foci at (+-5,0) is a. 16 x^2-9y^2=144 b. 9x^2-16 y^2=144 c. 25 x^2-9y^2=225 d. 9x^2-25 y^2=81

Find co - ordinates of foci, water length of major axis and minor aixs, eccentricity and length of latus rectum of following ellipse. Length of latus rectum of following ellipse. (1) 16x^(2) + 9y^(2) = 1 (2) 3x^(2) + 2y^(2) = 6 (3) 4x^(2) + 9y^(2) = 1 (4) (x^(2))/(49) + (y^(2))/(16) = 1 (5) 9x^(2) + 25y^(2) = 225 (6) 7x^(2) + 10y^(2) = 70 (7) 16x^(2) + 5y^(2) = 80

Prove that the locus of the mid -points of the chords of the circle x^(2)+y^(2)=16 which are tangents to the hyperbola 9x^(2)-16y^(2)=144 is (x^(2)+y^(2))^(2)=16x^(2)-9y^(2) .

If e_(1) and e_(2) represent the eccentricity of the curves 6x^(2) - 9y^(2) = 144 and 9x^(2) - 16y^(2) = 144 respectively . Then (1)/(e_(1)^(2)) + (1)/(e_(2)^(2)) is equal to

A common tangent to 9x^(2)-16y^(2)=144 and x^(2)+y^(2)=9, is

A common tangent to 9x^(2) - 16y^(2) = 144 and x^(2) + y^(2) = 9 is

If e_(1) and e_(2) represent the eccentricity of the curves 16x^(2)+9y^(2) = 144 and 9x^(2) - 16y^(2) = 144 respectively . Then