THETA DIVISION

Question 85

Analytic Geometry★★★★★Question Bank

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Question

The shortest distance between a point

(x_0,y_0)

and a line

Ax+By+C=0

is given by

\frac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}.

Let

S

be the set of all points

P

such that the distance from

P

(0,0)

is half the distance from

P

to the line

3x+4y=5

. There exist real numbers

A,B,C,D,

and

E

such that

S

is modeled by the equation

Ax^2+Bxy+Cy^2+Dx+Ey=1.

Compute

A+B+C+D+E

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