The equation of the tangent at the point (1/4 | vedclass

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Question

(D) Given the ellipse equation is $\frac{x^2}{4} + \frac{y^2}{12} = 1$. Check if the point $(1/4, 1/4)$ lies on the ellipse: Substitute $x = 1/4$ and

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) Given the ellipse equation is $\frac{x^2}{4} + \frac{y^2}{12} = 1$. Check if the point $(1/4, 1/4)$ lies on the ellipse: Substitute $x = 1/4$ and $y = 1/4$ into the equation: $\frac{(1/4)^2}{4} + \frac{(1/4)^2}{12} = \frac{1/16}{4} + \frac{1/16}{12} = \frac{1}{64} + \frac{1}{192} = \frac{3+1}{192} = \frac{4}{192} = \frac{1}{48}$. Since $\frac{1}{48} 
eq 1$,the point $(1/4, 1/4)$ does not lie on the ellipse. Therefore,the tangent at this point is not defined for this ellipse. Thus,the correct option is $D$.

The equation of the tangent at the point $(1/4, 1/4)$ of the ellipse $\frac{x^2}{4} + \frac{y^2}{12} = 1$ is

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