Geometria Analitica Conamat Ejercicios Resueltos Guide

: Set equal: [ x^2 = 2x + 3 \implies x^2 - 2x - 3 = 0 \implies (x - 3)(x + 1) = 0 ] [ x = 3 \implies y = 9 \quad \textand \quad x = -1 \implies y = 1 ]

: [ m = \frac9 - 34 - 1 = \frac63 = 2 ]

: Group ( x ) and ( y ) terms: [ (x^2 - 6x) + (y^2 + 4y) = 3 ] Complete the square: [ (x^2 - 6x + 9) + (y^2 + 4y + 4) = 3 + 9 + 4 ] [ (x - 3)^2 + (y + 2)^2 = 16 ] Center ( C(3, -2) ), radius ( r = 4 ). 7. Intersection of a Line and a Parabola ✅ Solved Exercise 7 Find intersection points between ( y = x^2 ) and ( y = 2x + 3 ). geometria analitica conamat ejercicios resueltos

: ( (x - 3)^2 + (y + 2)^2 = 16 ) 6. Circle from General Form to Standard Form ✅ Solved Exercise 6 Convert ( x^2 + y^2 - 6x + 4y - 3 = 0 ) to standard form and find center and radius.

: [ M_x = \frac-2 + 62 = \frac42 = 2, \quad M_y = \frac4 + (-8)2 = \frac-42 = -2 ] : Set equal: [ x^2 = 2x +

: [ d = \sqrt(7 - 3)^2 + (5 - 2)^2 = \sqrt4^2 + 3^2 = \sqrt16 + 9 = \sqrt25 = 5 ]

: [ (x - 3)^2 + (y + 2)^2 = 16 ]

: ( m = 2 ) 4. Equation of a Line (Point-Slope Form) Formula : [ y - y_1 = m(x - x_1) ] ✅ Solved Exercise 4 Find the line equation with slope ( m = -3 ) passing through ( (2, 5) ).

: ( d = 5 ) 2. Midpoint of a Segment Formula : [ M = \left( \fracx_1 + x_22, \fracy_1 + y_22 \right) ] ✅ Solved Exercise 2 Find the midpoint of ( P(-2, 4) ) and ( Q(6, -8) ). : ( (x - 3)^2 + (y + 2)^2 = 16 ) 6