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Problem 724

Write an equation for the circle with center \(\mathrm{A}(-3,-2)\) and radius 3.

Expert verified

\((x + 3)^2 + (y + 2)^2 = 9\)

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Chapter 42

Find the area of the ellipses (a) \(\mathrm{x}^{2} / 9+\mathrm{y}^{2} / 25=1\) (b) \(x^{2} / 144+y^{2} / 256=1\) (c) \(x^{2} / 64+y^{2} / 49=1\) (d) \(\mathrm{x}^{2} / 81+\mathrm{y}^{2} / 16=1\)

Chapter 42

Write the equation of the family of all concentric circles whose common center is the point \((-3,5)\). Draw three members of the family, specifying the value of the parameter in each case.

Chapter 42

For the ellipse \(36 \mathrm{x}^{2}+64 \mathrm{y}^{2}=2304\), sketch the ellipse and find the value of e and the coordinates of the vertices and foci.

Chapter 42

Write the equation of a circle with center at $\mathrm{C}(\mathrm{a}, \mathrm{b})\( and radius \)\mathrm{r}$.

Chapter 42

Given that two circles $\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{D}_{1} \mathrm{x}+\mathrm{E}_{1} \mathrm{y}+\mathrm{F}_{1}=0$ and $\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{D}_{2} \mathrm{x}+\mathrm{E}_{2} \mathrm{y}+\mathrm{F}_{2}=0$ intersect at two points, show that the equation for the line determined by the points of intersection is $\left(\mathrm{D}_{1}-\mathrm{D}_{2}\right) \mathrm{x}+\left(\mathrm{E}_{1}-\mathrm{E}_{2}\right)+\left(\mathrm{F}_{1}-\mathrm{F}_{2}\right)=0$.

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