Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Mathematics
Chapter
Hyperbola

BITSAT 2012 · Mathematics · Hyperbola

Find the eccentricity of the conic represented by x^ 2 -y^ 2 -4 x+4...

Find the eccentricity of the conic represented by x2−y2−4x+4y+16=0x^{2}-y^{2}-4 x+4 y+16=0

Options

  1. A2
  2. B2\sqrt{2}
  3. C222 \sqrt{2}
  4. D323 \sqrt{2}

Correct answer

B. 2\sqrt{2}

Step-by-step solution

We have x2−y2−4x+4y+16=0⇒(x2−4x)−(y2−4y)=16⇒(x2−4x+4)−(y2−4y+4)=−16⇒(x−2)2−(y−2)2=−16⇒(x−2)242−(y−2)242=1x^{2}-y^{2}-4 x+4 y+16=0\Rightarrow\left(x^{2}-4 x\right)-\left(y^{2}-4 y\right)=16\Rightarrow\left(x^{2}-4 x+4\right)-\left(y^{2}-4 y+4\right)=-16\Rightarrow(x-2)^{2}-(y-2)^{2}=-16\Rightarrow \frac{(x-2)^{2}}{4^{2}}-\frac{(y-2)^{2}}{4^{2}}=1 This is rectangular hyperbola, whose eccentricity is always 2\sqrt{2}.
Practice Hyperbola on Quantrex Academy →

More from Hyperbola

The foci of hyperbola 4 x^2-9 y^2-1=0 are BITSAT 2024The vertices of the hyperbola 9 x^2-16 y^2-36 x+96 y-252=0 are BITSAT 2023If the eccentricity and length of latus rectum of a hyperbola are 13 3 and (10)/(3) units… BITSAT 2023A tangent drawn to hyperbola (x2)/(a2) - (y2)/(b2) = 1 at P ((π)/(6)) forms a triangle of… BITSAT 2018If e _ 1 and e _ 2 are the eccentricities of a hyperbola 3x^ 2 - 3y^ 2 = 25 & and its… BITSAT 2018If equation ( 10x - 5 ) ^ 2 + ( 10y - 4 ) ^ 2 = λ ^ 2 ( 3x + 4y - 1 ) ^ 2 & represents a… BITSAT 2017 Full Hyperbola list Hyperbola JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs