Question

choose the origin (h,k) such that the equation 5x^2 -2y^2 -30x+8y=0 may reduce to the form Ax'^2+By'^2=1​

Answer 1

Step-by-step explanation:

Given equation :

$5 {x}^{2} - 2 {y}^{2} - 30x + 8y = 0$

To find :

The origin (h, k) for which the given equation may reduce to ;

$Ax'^2 + By'^2 = 1$

Solution :

$5 {x}^{2} - 2 {y}^{2} - 30x + 8y = 0$

$(5 {x}^{2} - 30x + 45) - 2 {y}^{2} + 8y - 8 - (45 - 8) = 0$

$=> 5( {x - 3)}^{2} - 2 {(y - 2)}^{2} - 37 = 0$

$=> \frac{5}{37} {(x - 3)}^{2} - \frac{2}{37} {(y - 2)}^{2} = 1$

$Here, Origin (h, k) = (3, 2). \\ </u></strong></p><p><strong><u>[tex]Here, Origin (h, k) = (3, 2). \\ A = \frac{5}{37} , \: \: B = \frac{ - 2}{37}$

Hence, the answer.