Question:
Which of the following is the equation of a hyperbola?
Which of the following is the equation of a hyperbola?
Updated On: May 18, 2024
- $x^2 - 4x + 16y + 17 = 0$
- $4x^2 + 4y2 - 16x + 4y -60 = 0$
- $x^2 + 2y^2 + 4x + 2y -27 = 0$
- $x^2 - y^2 + 3x - 2y -43 = 0$
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The Correct Option is D
Solution and Explanation
$x^{2}-y^{2}+3 x-2 y-43=0$
$=\left(x+\frac{3}{2}\right)^{2}-(y+1)^{2}-\frac{5}{4}-43=0$
$=\left(x+\frac{3}{2}\right)^{2}-(y+1)^{2}=\frac{177}{4}$
$=\frac{\left(x+\frac{3}{2}\right)^{2}}{\frac{177}{4}}-\frac{(y+1)^{2}}{\frac{177}{4}}=1$
It is hyperbola equation.
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Concepts Used:
Hyperbola
Hyperbola is the locus of all the points in a plane such that the difference in their distances from two fixed points in the plane is constant.
Hyperbola is made up of two similar curves that resemble a parabola. Hyperbola has two fixed points which can be shown in the picture, are known as foci or focus. When we join the foci or focus using a line segment then its midpoint gives us centre. Hence, this line segment is known as the transverse axis.
