# The curve passing through the points of intersection of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $x^2+y^2+2gx+2fy+c=0$

The curve passing through the points of intersection of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $x^2+y^2+2gx+2fy+c=0$ represents a pair of straight lines which are:
(a) equally inclined to the x axis
(b) perpendicular to each other
(c) pass through a fixed point
(d) none of the above

I am having a problem comprehending the question. How can the 2 intersection points define a whole curve? How can 2 distinct lines be defined by 2 intersection points?

• you will have for points of intersection. That cans give you two lines – Arnaldo Apr 6 '17 at 13:38
• @Arnaldo I tried it on geogebra and it gives only 2 points of intersection – Osheen Sachdev Apr 6 '17 at 13:39
• Be carefull to believe in geogebra. You will have an ellipse and a circle. You can get four points, it depends on the values of $a,b,c,g,f$ – Arnaldo Apr 6 '17 at 13:42
• @Arnaldo ah right...forgot that an ellipse and a circle can intersect in more than 2 points lol...you can post this as the answer – Osheen Sachdev Apr 6 '17 at 13:48

$$x^2+y^2+2gx+2fy+c=0\to (x+g)^2+(y+f)^2=g^2+f^2-c$$
That is a picture about what is happening according to the values of $a,b,c,f,g$.