Question

Find the equation of director circle of the conic 14x^2-4xy+11y^2-44x-58y-71=0

Answer 1

Step-by-step explanation:

The circle is the simplest and best known conic section. As a conic section, the circle is the intersection of a plane perpendicular to the cone's axis.

The geometric definition of a circle is the locus of all points a constant distance {\displaystyle r}from a point {\displaystyle (h,k)} and forming the circumference(C). The distance {\displaystyle r} is the radius (R) of the circle, and the point {\displaystyle O=(h,k)} is the circle's center also spelled as centre. The diameter (D) is twice the length of the radius.

Answer 2

Useful fact : For conic f(x,y) = 0 centre is found by solving ∂f/∂x = ∂f/∂y = 0

f(x,y) = 14x²−4xy+11y²−44x−58y+71

∂f/∂x = 28x−4y−44 = 0 → 7x−y = 11

∂f/∂y = −4x+22y−58 = 0 → −2x+11y = 29

These solve to give centre as (2,3)

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