The hyperbola `x^2/a^2 - y^2/b^2=1` passes through the point of intersection of the lines, `7x + 13y - 87 = 0 & 5x - 8y + 7 = 0` & the latus rectum is `32 sqrt2/5`. The value of `2(a^2 + b^2)` is :

The hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passes through the point of intersection of the lines,7x+13y-87=0&5x-8y+7=0 & the latus rectum is 32(sqrt(2))/(5). The value of 2(a^(2)+b^(2)) is :

The hyperbola x^2/a^2 - y^2/b^2 = 1 passes through the point of intersection of the lines 7x+ 13y-87=0 and 5x-8y+7=0 and its latus rectum is 32sqrt(2)/5 . Find a and b .

The hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 passes through the point of intersection of the lines 7x + 13y - 87 = 0 and 5x - 8y + 7 = 0 and its latus rectum is (32sqrt(2))/(5) Find a and b.

The ellipse x^2/a^2+y^2/b^2=1 passes through the point of intersection of the lines 7x+13y=87and 5x-8y+7=0and the length of its latus rectum is (32sqrt2)/5 units.Find the values of a and b.

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through the point of intersection of the lines 7x + 13 y - 87 = 0 and 5x - 8y + 7 = 0 and its length of latus rectum is (32sqrt(2))/(5) , find a and b .

If the ellipse x^2/a^2+y^2/b^2=1 passes through the intersecting points of two straight lines 7x + 13y -87=0 and 5x -8y + 7 = 0 and the'length of its latus rectum is (32sqrt2)/5 then find the value of a and b and also find its eccentricity

If the hyperhola x^2/a^2 - y^2/b^2 = 1 passes through the intersection of 7x+13y-87=0 and 5x-8y+7=0 and its latus rectum is 32sqrt(2)/(5) , then value of a and b are respectively. (A) 5/sqrt(3), 2 (B) 5/sqrt(2), 4 (C) 3/sqrt(2), 4 (D) 2, sqrt(3)/5

The hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 passes throught the point of intersection of the lines x - 3sqrt(5)y =0 and sqrt(5)x - 2y = 13 and the length of its latus rectum is (4)/(5) . Find the coordinates of its foci.

The hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passes through the point of intersection of the lines x-3sqrt(5)y=0 and sqrt(5)x-2y=13 and the length of its latus rectum is (4)/(3) units.The coordinates of its focus are