Chapter Exam

Unit 5: Hyperbola — Online MCQ Test

Q: What is the standard equation of a hyperbola with transverse axis along the x-axis and center at the origin?

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 \(x^2/a^2 - y^2/b^2 = 1\).

Q: In the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), what is the relation between \(c\), \(a\), and \(b\)?

Answer: B. \(c^2=a^2+b^2\) — For a hyperbola, the focal distance satisfies \(c^2=a^2+b^2\), unlike an ellipse.

Q: If a hyperbola is \(\frac{x^2}{9}-\frac{y^2}{16}=1\), what are its asymptotes?

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 \(b=4\).

Q: Which statement is NOT true for the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)?

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.

Q: For the hyperbola \(x^2-y^2=1\), which parametric form is correct?

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.

MATHEMATICS - 2B · CLASS 12 INTERMEDIATE 2 YEAR · Telangana State Board

Practice Unit 5: Hyperbola with a free chapter-wise online MCQ test for Telangana State Board CLASS 12 INTERMEDIATE 2 YEAR MATHEMATICS - 2B. This chapter covers: This chapter covers standard equation of hyperbola eccentricity foci directrices asymptotes conjugate hyperbola rectangular hyperbola and parametric representations.. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Unit 5: Hyperbola — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 12 INTERMEDIATE 2 YEAR MATHEMATICS - 2B — Unit 5: Hyperbola, with answers and explanations. These are sample questions; the exam has its own separate question set.

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 \(x^2/a^2 - y^2/b^2 = 1\).

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.

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 \(b=4\).

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.

For the hyperbola \(x^2-y^2=1\), which parametric form is correct?