Question

Match List-I with List-II for the hyperbola 

\[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \]

List-I	Element	List-II	Corresponding Value / Equation
A	Coordinate of centre	II	\((0,0)\)
B	One coordinate of vertex	I	\((a,0)\)
C	Equation of transverse axis	III	\(y=0\)
D	Equation of conjugate axis	IV	\(x=0\)

• A. A-I, B-II, C-III, D-IV
• B. A-I, B-II, C-IV, D-III
• C. A-II, B-I, C-III, D-IV
• D. A-II, B-I, C-IV, D-III

Hint:

For \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), transverse axis is \(y=0\) and conjugate axis is \(x=0\).

Answer 1

The Correct Option is C

Concept:
The standard hyperbola: \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] has transverse axis along \(x\)-axis.

Step 1: Centre. \[ \text{Centre}=(0,0) \] So: \[ A\rightarrow II \]

Step 2: Vertex. \[ \text{Vertices}=(\pm a,0) \] One coordinate of vertex is: \[ (a,0) \] So: \[ B\rightarrow I \]

Step 3: Transverse axis.
The transverse axis is the \(x\)-axis: \[ y=0 \] So: \[ C\rightarrow III \]

Step 4: Conjugate axis.
The conjugate axis is the \(y\)-axis: \[ x=0 \] So: \[ D\rightarrow IV \] \[ \therefore \text{Correct Answer is (C)} \]