Question

The equation of the ellipse which passes through the origin and has its foci at the points $(1,0)$ and $(3,0)$ is $p{x}^2+q{y}^2+rx=0$. Find the value of $p+q+r.$

• A. $-4$
• B. $-5$
• C. $4$
• D. $5$

Answer 1

The correct option is B $-5$

Centre being mid-point of foci is $(2,0)$

Distance between foci $=2=2ae$ $\therefore a^2{e}^2=1$ or $a^2-b^2=1$ ...(1)
Thus the ellipse is of the form $\frac{{(x-2)}^2}{a^2}+\frac{y^2}{b^2}=1$
Now as it passes through $(0,0)\therefore \frac{4}{a^2}=1$
or $a^2=4\therefore b^2=3$ by (1)
Hence ellipse is, $\frac{{(x-2)}^2}{4}+\frac{y^2}{3}=1$ or $3x^2+4y^2-12x=0$