If the focii of x² 16 + y² 4 =1 and x² a² - y² 9 =1 coincide, then the value of a is

Step-by-step solution

Equation of conics x² 16 + y² 4 =1, x² a² - y² 9 =1 Equation of eccentricity of an ellipse aligned b² &=a² (1-e² ) 4 &=16 (1-e² ) e² &=1-1 / 4=3 / 4 e &= 3 4 Focii of an ellipse &=( a e, 0) &= ( 4 3 2 , 0 )=( 2 3 , 0) aligned Given, focii of both conics are coincides. ( 2 3 , 0)=( a e, 0) [ Here ( a e, 0) is focii of second conic.] a e= 2 3 a² e²=12 Equation of eccentricity of second conic (hyperbola) aligned &b²=a² (e²-1 ) &b²=a² e²-a² aligned b²=a² e²-a² array ll & 9=12-a² & a²=3 a= 3 array