MAT103/113 General Mathematics III Practice Flashcards

A collection of practice flashcards covering coordinate geometry, including slopes, circle equations, and parabola properties based on the MAT103/113 E-Test Questions from Federal University of Technology Minna.

What is the slope of the line passing through points $M(5, -2)$ and $N(-4, -6)$?

$$\frac{4}{9}$$

What is the linear form equation of a line passing through the point $(-2, 5)$ where $\frac{dy}{dx} = 10$?

$$y = 10x + 25$$

According to the transcript, which form of the equation of a straight line is represented by $\frac{x}{a} + \frac{y}{b} = 1$?

Intercept form

What are the center and radius of the circle defined by the equation $x^2 + y^2 - 6x + 4y - 3 = 0$?

Center $(3, -2)$, Radius $4$

What is the equation of the tangent to the parabola $y^2 = 8x$ at the point $(2, 4)$?

$$y = x + 2$$

What is the equation of the tangent to the circle $x^2 + y^2 = 169$ at the point $(12, -5)$?

$$5y = 12x - 169$$

What are the vertex and focus of the parabola $(y - 2)^2 + 16(x - 3) = 0$?

Vertex $(3, 2)$, Focus $(-1, 2)$

What is the perpendicular distance between the point $(1, 3)$ and the line $12y + 5x = -4$?

$$\frac{35}{13}$$

What is the distance between the points $P(k, 2k)$ and $Q(-3k, -k)$?

$$5k$$

What is the equation of the normal to the parabola $y^2 = 18x$ at point $(2, 6)$?

$$3y + 2x = 22$$

What is the midpoint coordinate of the line joining the points $M(-4, 3)$ and $N(6, 7)$?

$$(1, 5)$$

What is the value of $\tan(\phi)$ where $\phi$ is the angle between the lines $3y = -4x + 7 = 0$ and $2y + 6x + 12 = 0$?

$$\frac{3}{4}$$

What are the vertex and focus of the parabola $y^2 = -\frac{9}{8}x$?

Vertex $(0, 0)$, Focus $(-\frac{9}{32}, 0)$

What is the distance between point $A(3k, 6k)$ and point $B(3k, -3k)$?

$$9k$$

What is the vertex and directrix of the parabola transcribed as $x = \frac{1}{4y^2}$ (where the answer key indicates $y^2 = -4x$ logic)?

Vertex $(0, 0)$, Directrix $x = 1$

What are the vertex and focus of the parabola $y^2 = 12x$ at the point $(3, 2)$ (as labeled in the transcript)?

Vertex $(0, 0)$, Focus $(3, 0)$

What is the directrix of the parabola $4y + x^2 = 0$?

$$y = 1$$

What are the center and radius of the circle with the equation $x^2 + y^2 = 5$?

Center $(0, 0)$, Radius $\sqrt{5}$

What is the tangent of the angle between the lines $y = -2x - 9$ and $2y = 7x + 4$?

$$\frac{11}{12}$$

What is the gradient of line $UV$ given the points $U(+\frac{1}{2}, \frac{3}{4})$ and $V(\frac{1}{4}, \frac{1}{2})$ as per the provided key?

$$-\frac{11}{40}$$