Graph the Polar equation r 5 5 cos theta identify the coni

Graph the Polar equation r = 5 + 5 cos theta identify the conic section, then graph; 4x^2 + 25y^2 + 8x-100 y + 4 = 0 Find a so that the vectors v = i - aj and w = 2i - 3j are orthogonal Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. 100 y^1 - 81 x^2 = 8100

Solution

4x^2 +25y^2+8x-100y+4=0

4(x^2 +2x+1-1) +25(y^2 -4y+4-4)=-4

4(x+1)^2 +25(y-2)^2=-4+4+100

(x+1)^2 /25 + (y-2)^2/4=1

Its an ellipse

Next question

v=i-a j

W=2i-3j

Vectors are orthogonal,it means dot product is 0.

2-3a=0

a=2/3