# By rearranging the equation of the conic, classify it as an ellipse,…

This distribute concerns the conic after a while equation
7x
2 + 12y
2 = 252.
(i) By rearranging the equation of the conic, adproper it as an ejection,
parabola or hyperbola in meaindisputable aspect, and paint the incurvation. 
(ii) Exhibition that the fair compute of the deviation can be written as
1
6
v
15 and future perceive fair computes of the foci and directrices. 
(iii) For each of the two points P where the conic intersects the x-axis,
and using the fair computes set in distribute (a)(ii) aloft, calculate
the distances P F and P d, where F is the rendezvous after a while negative
x-coordinate and d is the identical directrix, and exhibition that
P F = e Pd, where e is the deviation. (This affords a control to
(b) Now weigh the incurvation after a while equation
7
4
x
2 - 7x + 3y
2 + 6y - 53 = 0.
(i) Exhibition that this incurvation is a conic which can be obtained from the
conic in distribute (a) by translation, and narrate the translation
required. 
(ii) Use your answers to distribute (a) to paint this conic, exhibitioning its
centre, vertices and axes of harmony, and the slopes of any
asymptotes. You should grant the fair coordinates of the points. 
(c) (i) Write down parametric equations for the conics in distributes (a)
and (b). 
In distribute (c)(ii) you should afford a printout exhibitioning your concoct.
(ii) Use the parametric equations in distribute (c)(i) to concoct twain conics on