Equation of the hyperbola with foci `(0,pm5)` and `e=(5)/(3)` is
(1)`(x^(2))/(9)-(y^(2))/(16)=1` (2)`(x^(2))/(16)-(y^(2))/(9)=-1`
(3)`(x^(2))/(16)-(y^(2))/(9)=1`(4)`(x^(2))/(12)-(y^(2))/(13)=1`

The equation of the ellipse having a vertex at (6,1) a focus at (4,1) and the eccentricity (3)/(5) is 1) ((x-1)^(2))/(16)+((y-1)^(2))/(25)=1 (2) ((x-1)^(2))/(25)+((y-1)^(2))/(16)=1 3) ((x+1)^(2))/(25)+((y+1)^(2))/(16)=1 (4) ((x+1)^(2))/(16)+((y+1)^(2))/(25)=1

The slopes of the common tangents of the hyperbolas (x^(2))/(9)-(y^(2))/(16)=1 and (y^(2))/(9)-(x^(2))/(16)=1 , are

The length of common tangent to the ellipses (x^(2))/(16)+(y^(2))/(9)=1 and (x^(2))/(9)+(y^(2))/(16)=1 is

Statement 1: Two ellipses (x^(2))/(16)+(y^(2))/(9)=1 and (x^(2))/(9)+(y^(2))/(16)=1 are congruent.Statement 2:(x^(2))/(16)+(y^(2))/(16)=1 and (x^(2))/(9)+(y^(2))/(16)=1 have same eccentricity

Area of quadrilateral formed by common tangents to ellipses E_(1):(x^(2))/(16)+(y^(2))/(9)=1 and E_(2):(x^(2))/(9)+(y^(2))/(16)=1 is

Locus of feet of perpendicular from (5,0) to the tangents of (x^(2))/(16)-(y^(2))/(9)=1 is (A)x^(2)+y^(2)=4(B)x^(2)+y^(2)=16(C)x^(2)+y^(2)=9(D)x^(2)+y^(2)=25

the centre of the ellipse ((x+y-2)^(2))/(9)+((x-y)^(2))/(16)=1 , is

The mid point of the chord 16x+9y=25 to the ellipse (x^(2))/(9)+(y^(2))/(16)=1 is

If the foci of (x^(2))/(16)+(y^(2))/(4)=1 and (x^(2))/(a^(2))-(y^(2))/(3)=1 coincide, the value of a is

Locus of feet of perpendiculars drawn from either foci on a variable tangent to hyperbola 16y^(2)-9x^(2)=1 is (A)x^(2)+y^(2)=9(B)x^(2)+y^(2)=(1)/(9)(C)x^(2)+y^(2)=(7)/(144)(D)x^(2)+y^(2)=(1)/(16)