# SOLUTION: 1Find the vertex and focus of the parabola whose equation is 4y = x2 + 4. aV(0, 4), F(0, 3) bV(0, 1), F(0, 2) cV(4, 0), F(3, 0) dV(1, 0), F(2, 0) 2Find the center and

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 1Find the vertex and focus of the parabola whose equation is 4y = x2 + 4. aV(0, 4), F(0, 3) bV(0, 1), F(0, 2) cV(4, 0), F(3, 0) dV(1, 0), F(2, 0) 2Find the center and      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Mathway solves algebra homework problems with step-by-step help!

 Algebra: Complex Numbers Solvers Lessons Answers archive Quiz In Depth

 Question 486499: 1Find the vertex and focus of the parabola whose equation is 4y = x2 + 4. aV(0, 4), F(0, 3) bV(0, 1), F(0, 2) cV(4, 0), F(3, 0) dV(1, 0), F(2, 0) 2Find the center and radius of the circle whose equation is x2 + 10x + y2 = 75. aC(10, 0), r = 100 bC(10, 0), r = 10 cC(5, 0), r = 100 dC(5, 0), r = 10 3Find the foci of the ellipse with the following equation. ((x-1)2÷9)+((Y+2)2÷25)=1 aF1(5, 2), F2(3, 2) bF1(1, 2), F2(1, 6) cF1(4, 2), F2(2, 2) dF1(1, 1), F2(1, 5) 4Find the slopes of the asymptotes of a hyperbola with the following equation. (Y2÷81)-(x2÷64)=1 a8/9 b9/8 c8/9, 8/9 d9/8, 9/8 Answer by lwsshak3(7679)   (Show Source): You can put this solution on YOUR website!1Find the vertex and focus of the parabola whose equation is 4y = x2 + 4. 2Find the center and radius of the circle whose equation is x2 + 10x + y2 = 75. 3Find the foci of the ellipse with the following equation. ((x-1)2÷9)+((Y+2)2÷25)=1 4Find the slopes of the asymptotes of a hyperbola with the following equation. (Y2÷81)-(x2÷64)=1 *** 1) Find the vertex and focus of the parabola whose equation is 4y = x^2 + 4. y=x^2/4+4/4 y=x^2/4+1 y=(1/4)(x^2)+1 x^2/4=y-1 x^2=4(y-1) This is an equation of a parabola of standard form: (x-h)^2=4p(y-k), (h, k) being the (x, y) coordinates of the vertex. Parabola has a vertical axis of symmetry and it opens upwards. For given equation: vertex: (0,1) .. 4p=4 p=1 focus: (0,2) ans:bV(0, 1), F(0, 2) .. 2) Find the center and radius of the circle whose equation is x2 + 10x + y2 = 75. x^2+10x+y^2=75 complete the square (x^2+10x+25)+(y^2)=75+25=100 (x+5)^2+(y+0)^2=100 center:(-5,0) radius=√100=10 ans:dC(5, 0), r = 10 .. 3) Find the foci of the ellipse with the following equation. ((x-1)2/9)+((Y+2)2/25)=1 This is an equation of an ellipse with vertical major axis of the standard form: (x-h)^2/b^2+(y-k)^2/a^2=1, a>b, with (h,k) being the (x,y) coordinates of the center. center: (1,-2) a^2=25 b^2=9 c^2=a^2-b^2=25-9=16 c=√16=4 Foci: (1,-2ħc)=(1,-2ħ4)=(1,2) and (1,-6) ans: bF1(1, 2), F2(1, 6) .. 4Find the slopes of the asymptotes of a hyperbola with the following equation. (Y2/81)-(x2/64)=1 This is an equation of a hyperbola with vertical transverse axis of the standard form: (y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center For given equation: Center: (0,0) a^2=81 a=√81=9 .. b^2=64 b=√64=8 slope of asymptotes=ħa/b=ħ9/8 ans: d9/8, 9/8