Find the polar equation of the circle, if its center is at \((4,0)\) and the radius \(4\).
A\(r-8 \cos \theta=0\)
B\(r-6 \cos \theta=0\)
C\(r-12 \cos \theta=0\)
D\(r-4 \cos \theta=0\)
Mathematics · Question Bank
Analytic Geometry
89 of 233 questions match · page 5 of 5. Answer in your head first, then check the solution.
What are the x and y coordinates of the focus of the conic section described by the following equation? (Angle \(\theta\) corresponds to a right triangle with adjacent side x, opposite side y and the hypotenuse r.) \(r \sin^2 \theta=\cos \theta\)
A(1/4, 0)
B(0, \(\pi/2\))
C(0, 0)
D(-1/2, 0)
Find the polar equation of the circle of radius \(3\) units and center at \((3,0)\).
A\(r=3 \cos \theta\)
B\(r=3 \sin \theta\)
C\(r=6 \cos \theta\)
D\(r=9 \sin \theta\)
Given the polar equation \(r=5 \sin \theta\). Determine the rectangular coordinates (x,y) of a point in the curve when \(\theta\) is \(30^\circ\).
A(2.17, 1.25)
B(3.08, 1.5)
C(2.51, 4.12)
D(6,3)
Find the standard equation of the circle with the center at (1, 3) and tangent to the line \(5x - 12y - 8 = 0\).
A\((x-1)^2 + (y-3)^2 = 8\)
B\((x-1)^2 + (y-3)^2 = 12\)
C\((x-1)^2 + (y-3)^2 = 9\)
D\((x-1)^2 + (y-3)^2 = 23\)
If the parabola \(y = x^2 + C\) is tangent to the line \(y = 4x + 3\), find the value of C.
A4
B7
C6
D5
What is the equation of the normal to the curve \(x^2 + y^2 = 25\) at (4, 3)?
A4x + 3y = 25
B3x − 4y = 0
C4x − 3y = 7
D3x + 4y = 24
The eccentricity of the hyperbola having the rectangular equation \(3x^2 - 4y^2 - 24x + 16y + 20 = 0\) is
A1.12
B1.22
C1.32
D1.42
The cross-section of a trough is a semi-ellipse with a width at the top of 18 cm and a depth of 12 cm. The trough is filled with water to a depth of 8 cm. Find the width at the surface of the water.
A\(5\sqrt{2}\) cm
B\(12\sqrt{2}\) cm
C\(7\sqrt{2}\) cm
D\(6\sqrt{2}\) cm