Unit 5: Hyperbola — Online MCQ Test
MATHEMATICS - 2B · CLASS 12 INTERMEDIATE 2 YEAR · Telangana State Board
Practice Unit 5: Hyperbola with a free chapter-wise online MCQ test.
This chapter covers: This chapter covers standard equation of hyperbola eccentricity foci directrices asymptotes conjugate hyperbola rectangular hyperbola and parametric representations..
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Unit 5: Hyperbola — Important Questions & Answers
What is the standard equation of a hyperbola with transverse axis along the x-axis and center at the origin?
- A. \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)
- B. \(\frac{y^2}{a^2}-\frac{x^2}{b^2}=1\)
- C. \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
- D. \(x^2+y^2=a^2\)
Answer: A. \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)
A hyperbola centered at the origin with transverse axis along the x-axis has the form \(x^2/a^2 - y^2/b^2 = 1\).
A hyperbola centered at the origin with transverse axis along the x-axis has the form \(x^2/a^2 - y^2/b^2 = 1\).
In the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), what is the relation between \(c\), \(a\), and \(b\)?
- A. \(c^2=a^2-b^2\)
- B. \(c^2=a^2+b^2\)
- C. \(c=a+b\)
- D. \(c^2=b^2-a^2\)
Answer: B. \(c^2=a^2+b^2\)
For a hyperbola, the focal distance satisfies \(c^2=a^2+b^2\), unlike an ellipse.
For a hyperbola, the focal distance satisfies \(c^2=a^2+b^2\), unlike an ellipse.
If a hyperbola is \(\frac{x^2}{9}-\frac{y^2}{16}=1\), what are its asymptotes?
- A. \(y=\pm \frac{4}{3}x\)
- B. \(y=\pm \frac{3}{4}x\)
- C. \(x=\pm \frac{4}{3}y\)
- D. \(x=\pm \frac{3}{4}y\)
Answer: A. \(y=\pm \frac{4}{3}x\)
The asymptotes of \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) are \(y=\pm \frac{b}{a}x\). Here \(a=3\) and \(b=4\).
The asymptotes of \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) are \(y=\pm \frac{b}{a}x\). Here \(a=3\) and \(b=4\).
Which statement is NOT true for the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)?
- A. Its foci lie on the x-axis
- B. Its asymptotes pass through the origin
- C. Its directrices are parallel to the y-axis
- D. Its eccentricity is less than 1
Answer: D. Its eccentricity is less than 1
A hyperbola always has eccentricity greater than 1, so the statement saying it is less than 1 is false.
A hyperbola always has eccentricity greater than 1, so the statement saying it is less than 1 is false.
For the hyperbola \(x^2-y^2=1\), which parametric form is correct?
- A. \(x=\sec t,\ y=\tan t\)
- B. \(x=\cos t,\ y=\sin t\)
- C. \(x=\tan t,\ y=\sec t\)
- D. \(x=t,\ y=t^2\)
Answer: A. \(x=\sec t,\ y=\tan t\)
Since \(\sec^2 t-\tan^2 t=1\), the parametric form \(x=\sec t, y=\tan t\) satisfies the hyperbola.
Since \(\sec^2 t-\tan^2 t=1\), the parametric form \(x=\sec t, y=\tan t\) satisfies the hyperbola.