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Mathematics Question on Hyperbola

Which of the following is the equation of a hyperbola?

A

x2−4x+16y+17=0x^2 - 4x + 16y + 17 = 0

B

4x2+4y2−16x+4y−60=04x^2 + 4y2 - 16x + 4y -60 = 0

C

x2+2y2+4x+2y−27=0x^2 + 2y^2 + 4x + 2y -27 = 0

D

x2−y2+3x−2y−43=0x^2 - y^2 + 3x - 2y -43 = 0

Answer

x2−y2+3x−2y−43=0x^2 - y^2 + 3x - 2y -43 = 0

Explanation

Solution

x2−y2+3x−2y−43=0x^{2}-y^{2}+3 x-2 y-43=0 =(x+32)2−(y+1)2−54−43=0=\left(x+\frac{3}{2}\right)^{2}-(y+1)^{2}-\frac{5}{4}-43=0 =(x+32)2−(y+1)2=1774=\left(x+\frac{3}{2}\right)^{2}-(y+1)^{2}=\frac{177}{4} =(x+32)21774−(y+1)21774=1=\frac{\left(x+\frac{3}{2}\right)^{2}}{\frac{177}{4}}-\frac{(y+1)^{2}}{\frac{177}{4}}=1 It is hyperbola equation.