Analytical Geometry Mathematics & Economics Math Problem (Math Problem Sample)

BMA 1205 Analytical Geometry C.A.T
Charles Opija
Name of Institution

BMA 1205 ANALYTICAL GEOMETRY CAT
The equation of a parabola x2+4x+ 6y-8=0.Find the vertex and the focus of the parabola. (3mks)
Solution
x2+4x = 6y + 8
(x +2)2 = -6y + 8 +4
(x +2)2 = -6y + 12
(x +2)2 = -6(y - 2)
4p = -6
p = -6/4
p = -3/2 vertex (-2,2) directrix -1.5
i. Find the equations of the tangents to the circle (x-4)2+(y-5)2=20 if the tangent has a slope of 2. (2mks)
solution
gradient of the radius = -1/2
 QUOTE

 = -1/2 x =6 and y = - 4
 QUOTE

 = 2 ; y = 2x -16
ii. Find the equations of the normal to the circle above at the point of tangency. (2mks)
 QUOTE

 = -1/2


A parallelogram MNPQ has vertices M (-7,3) N (2,2) P (4, -2) Q(-5,-1) i. Find the equation of lines NP and PQ ( 2mks)
 QUOTE

 =  QUOTE


 QUOTE

 = -2
y-2=-2x+4
NP: y = -2x+6
 QUOTE

= QUOTE