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Statement-1 : Tangents drawn from the po...

Statement-`1` : Tangents drawn from the point `(2,-1)` to the hyperbola `x^(2)-4y^(2)=4` are at right angle. Statement-`2` : The locus of the point of intersection of perpendicular tangents to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` is the circle `x^(2)+y^(2)=a^(2)-b^(2)`.

A

`1`

B

`2`

C

`3`

D

`4`

Text Solution

AI Generated Solution

To solve the problem, we need to analyze both statements provided. ### Step 1: Analyze Statement 1 We are given the hyperbola \( x^2 - 4y^2 = 4 \). We can rewrite it in standard form: \[ \frac{x^2}{4} - \frac{y^2}{1} = 1 \] Here, \( a^2 = 4 \) and \( b^2 = 1 \), thus \( a = 2 \) and \( b = 1 \). ...
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