# Analytic geometry questions and answers

Recent questions in Analytic geometry
Analytic geometry

### A figure is made up of a triangle and a square, where the triangle's base $$\displaystyle{\left({\underset{{\triangle}}{{{b}}}}\right)}$$ is a side of a square $$\displaystyle{\left({\underset{{\boxempty}}{{{l}}}}\right)}$$. $$\displaystyle{\underset{{\triangle}}{{{h}}}}={8}{c}{m}$$ $$\displaystyle{\underset{{\triangle}}{{{l}}}}={\underset{{\triangle}}{{{s}}}}={10}{c}{m}$$ $$\displaystyle{\underset{{{f}{i}{g}{u}{r}{e}}}{{{P}}}}={56}{c}{m}$$ $$\displaystyle{\underset{{{f}{i}{g}{u}{r}{e}}}{{{A}}}}=?$$

Analytic geometry

### Find the area of the parallelogram with vertices A(-3, 0), B(-1 , 3), C(5, 2), and D(3, -1).

Analytic geometry

### Find the area enclosed by the curve $$\displaystyle{x}={t}^{{2}}-{2}{t},\ {y}=\sqrt{{{t}}}$$ and the y-axis

Analytic geometry

### Find the area of the shaded region. $$\displaystyle{r}^{{2}}={\sin{{\left({2}\theta\right)}}}$$

Analytic geometry

### A bridge is built in the shape of a parabolic arch. The bridge has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center.

Analytic geometry

### Write the area A of a square as a function of its peremiter P.

Analytic geometry

### Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(2, 3, 2), R(1, 4, -1), S(3, 6, 1)

Analytic geometry

### Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection. $$\displaystyle{L}_{{1}}:{\frac{{{x}-{2}}}{{{1}}}}={\frac{{{y}-{3}}}{{-{2}}}}={\frac{{{z}-{1}}}{{-{3}}}}$$

Analytic geometry

### Find the area enclosed by the curve $$x=t^2-2t,\ y=\sqrt{t}$$ and the y-axis

Analytic geometry

### Find the area of the parallelogram with vertices A(-3, 0), B(-1 , 3), C(5, 2), and D(3, -1).

Analytic geometry

### A bridge is built in the shape of a parabolic arch. The bridge has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center.

Analytic geometry

### Write the area A of a square as a function of its peremiter P.

Analytic geometry

### Find the area of the shaded region. $$r^2 = \sin (2 \theta)$$

Analytic geometry

### Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(2, 3, 2), R(1, 4, -1), S(3, 6, 1)

Analytic geometry

### Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection. $$L_1: \frac{x-2}{1}=\frac{y-3}{-2}=\frac{z-1}{-3}$$

Analytic geometry

### Trace the curve $$\displaystyle{y}=\frac{{x}}{{{x}-{1}}}{\left({x}+{3}\right)}$$

Analytic geometry

### Trace the curve $$\displaystyle{r}^{{2}}={4}{{\cos}^{\theta}{{\tan}^{{2}}\theta}}$$

Analytic geometry

### Find an equation of the plane passing through the three points given. $$P = (2, 0, 0),$$ $$Q = (0, 4, 0),$$ $$R = (0, 0, 2)$$

Analytic geometry