The question I am stuck on is (iii):
This part concerns the conic with equation
(i) By rearranging the equation of the conic, classify it as an ellipse, parabola or hyperbola in standard position, and sketch the curve.
I have re-arranged the equation and discovered it is an ellipse in standard position:
The points of the ellipse are (-5,0), (0, ), (5,0) and (0, )
(ii) Find exact values for the eccentricity, foci and directrices of this conic, and mark the foci and directrices on your sketch.
eccentricity (e) = =
foci = +-ae = and
directrices = +-a/e =
(iii) Check your answers to part (a)(ii) by verifying that the equation PF = ePd holds at each of the two points P where the conic intersects the x-axis, where F is the focus with negative x-coordinate, d is the corresponding directrix and e is the eccentricity.
point, P where the conic intersect the x-axis ... etc. (-5,0)
focus with negative x co-ordinate =
corresponding directrix =
I know that PF = a-ae =
and ePd = e(a-ae)/e =
so PF = ePd, but I'm not sure what they mean when they say the two points, P where the conic intersects the x-axis ... etc.
I hope what I have done so far is correct? Thanks again for your help. It is most appreciated