Analytic Geometry

A tangent to a conic is a line

Find the area of the triangle which the line \(2x - 3y + 6 = 0\) forms with the coordinate axes.

If the vertex of \(y = 2x^2 + 4x + 5\) is shifted 3 units to the left and 2 units downward, what will be the new location of the vertex?

In the polar coordinate system, the distance from a point to the pole is known as the

If the equation is unchanged by the substitution of −x for x, its curve is symmetric with respect to the

What conic section is represented by \(2x^2 + y^2 - 8x + 4y = 16\)?

What is the length of the line with a slope of 4/3 from a point (6, 4) to the y-axis?

The inclination of the line determined by the points (4, 0) and \((5, \sqrt{3})\) is

How many petals are there in the rose curve \(r = 3\cos 5\theta\)?

A conic section whose eccentricity is equal to one (1) is known as

In a conic section, if the eccentricity is greater than one (1), the locus is

How far is the directrix of the parabola \((x - 4)^2 = -8(y - 2)\) from the x-axis?

The equations of two lines are \(3y - 2x = 6\) and \(3x + ky = -7\). For what value of k will the two lines be parallel?

The vertex of the parabola \(y = (x - 1)^2 + 2\) is ______.

In an ellipse, a chord which contains a focus and is in a line perpendicular to the major axis is a:

What kind of graph has \(r = 2\sec\theta\)?

The axis of the hyperbola through its foci is known as the

Classify the graph of the equation \(x^2 + xy + y^2 - 6 = 0\).

A parabola having its axis along the x-axis passes through (−3, 6). Compute the length of the latus rectum if the vertex is at the origin.

Points (6, −2) and (a, 6) are on a line with a slope of 4/3. What is the value of a?