Question

Which of the given statements is/are not correct?

• A. The equation of an ellipse with foci on the x-axis to is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
• B. Length of the latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $\frac{2a^2}{b}$
• C. Equation of the parabola with vertex at the origin, focus at (a, 0) and directrix $x=-a$ is $y^2=4ax$.
• D. Length of the latus rectum of the parabola $x^2=-4ay$ is 2a.

Answer 1

Answer: (B), (D)

Length of the latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $\frac{2a^2}{b}$
Length of the latus rectum of the parabola $x^2=-4ay$ is 2a.

Eqation of ellipse $\Rightarrow \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Length of latus rectum of ellipse $\Rightarrow \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $l$ = 2$\frac{(minoraxis{)}^2}{\left(majoraxis\right)}$

latus rectum of parabola $x^2$ = $-4ay=2a$

Equation of the parabola with vertex at the origin, focus at(a,0) and directric $y=a$ is $x^2$ = $-4ax$

Hence, Length of latus rectum of ellipse $\Rightarrow \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $\frac{(2a{)}^2}{\left(b\right)}$

Hence, latus rectum of parabola $x^2$ = $-4ay$ is $2a$