Conamat Ejercicios Resueltos — Geometria Analitica

: ( y = -3x + 11 ) 5. Equation of a Circle (Center and Radius) Standard form : [ (x - h)^2 + (y - k)^2 = r^2 ] Center ( C(h, k) ), radius ( r ). ✅ Solved Exercise 5 Find the equation of the circle with center ( C(3, -2) ) and radius ( r = 4 ).

: 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 ).

: ( M(2, -2) ) 3. Slope of a Line Formula : [ m = \fracy_2 - y_1x_2 - x_1 ] ✅ Solved Exercise 3 Find the slope through ( A(1, 3) ) and ( B(4, 9) ). geometria analitica conamat ejercicios resueltos

: [ y - 5 = -3(x - 2) \implies y - 5 = -3x + 6 \implies y = -3x + 11 ]

The article includes theory reminders, step-by-step solved problems, and practical tips. Analytic geometry combines algebra and geometry to study geometric figures using coordinates and equations. It is essential for understanding lines, circles, parabolas, ellipses, and hyperbolas. : ( y = -3x + 11 ) 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 ]

: ( (3, 9) ) and ( (-1, 1) ) 8. Parabola Vertex, Focus, Directrix Vertical parabola : ( (x - h)^2 = 4p(y - k) ) Vertex ( (h, k) ), focus ( (h, k + p) ), directrix ( y = k - p ). ✅ Solved Exercise 8 Find vertex, focus, directrix of ( y = 2x^2 - 8x + 5 ).