AssertionA- The difference of the focal distances of any point on the hyperbola x2-36-y2-9-1 is 12-ReasonR- The difference of the focal distances of any point on the hyperbola is equal to the length of it transverse axis

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Byju's Answer

Standard XII

Mathematics

Focii of Hyperbola

AssertionA: T...

Question

Assertion(A): The difference of the focal distances of any point on the hyperbola $\frac{x^{2}}{36} - \frac{y^{2}}{9} = 1$ is 12.
Reason(R): The difference of the focal distances of any point on the hyperbola is equal to the length of it transverse axis

Both A and R are true and R is the correct
explanation of A.

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Both A and R are true but R is not the correct
explanation of A.

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A is true but R is false.

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A is false but R is true.

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Solution

The correct option is A Both A and R are true and R is the correct
explanation of A.
Clearly, $| S P - S^{'} P | = 2 a = 12$
Thus statement 1 is correct.
Also statement 2 is correct and followed by statement 1.

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Assertion(A): The difference of the focal distances of any point on the hyperbola x236−y29=1 is 12.Reason(R): The difference of the focal distances of any point on the hyperbola is equal to the length of it transverse axis

The correct option is A Both A and R are true and R is the correctexplanation of A.Clearly, |SP−S′P|=2a=12Thus statement 1 is correct.Also statement 2 is correct and followed by statement 1.

Assertion(A): The difference of the focal distances of any point on the hyperbola $\frac{x^{2}}{36} - \frac{y^{2}}{9} = 1$ is 12.
Reason(R): The difference of the focal distances of any point on the hyperbola is equal to the length of it transverse axis

The correct option is A Both A and R are true and R is the correct
explanation of A.
Clearly, $| S P - S^{'} P | = 2 a = 12$
Thus statement 1 is correct.
Also statement 2 is correct and followed by statement 1.