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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Ellipse

NDA 2023 · Mathematics · Ellipse

Consider the following in respect of the equation...

Consider the following in respect of the equation x224−k+y2k−16=21.Theequationrepresentsanellipseifk=19\frac{x^2}{24-k}+\frac{y^2}{k-16}=2 1. The equation represents an ellipse if \mathrm{k}=19. 2. The equation represents a hyperbola if k=123.Theequationrepresentsacircleif\mathrm{k}=12 3. The equation represents a circle if k=20Howmanyofthestatementsgivenabovearecorrect?How many of the statements given above are correct?

Options

  1. AOnly one
  2. BOnly two
  3. CAll three
  4. DNone

Correct answer

C. All three

Step-by-step solution

Given the equation x224−k+y2k−16=2\frac{x^2}{24-k}+\frac{y^2}{k-16}=2 If k=19⇒k=19 \Rightarrow Given equation is ellipse. If k=12⇒\mathrm{k}=12 \Rightarrow Given equation is hyperbola If k=20⇒\mathrm{k}=20 \Rightarrow Given equation is circle
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