Senior High School 1st Quarter Prelim Exam

Questions and Answers

Which of the following ordered pairs represents the center of circle C?

(y, k)

(h, k) (correct)

(x, y)

(x, h)

When the radius is equal to zero, what will happen to the graph of the circle?

The graph is a single point. (correct)

The graph is out of round.

There is no graph since the radius is imaginary.

The graph is still the same.

Find the standard form of the equation of the parabola given that the vertex is at (-3, -1) and the directrix is y = -3.

(x + 3)^2 = (y - 1)

(x - 1)^2 = -4(y + 1)

(x + 1)^2 = -(y + 3)

(x + 3)^2 = -(y + 1) (correct)

What is the equation of the parabola whose vertex is at the center of $x^2 + y^2 - 10x + 4y - 5 = 0$ and whose focus is on the y-axis?

(y + 2)^2 = -20(x - 5) Signup and view all the answers

What is the line segment joining the vertices of a hyperbola?

Transverse axis Signup and view all the answers

What is TRUE about hyperbolas?

The pair of straight lines drawn parallel to the hyperbola is called the asymptote. Signup and view all the answers

Find the equation of an ellipse with center at (2, 2), horizontal major axis, focal distance of length 20 units, and minor axis of length 42 units.

$(x - 2)^2/(841) + (y - 1)^2/(441) = 1$ Signup and view all the answers

Study Notes

Circle and Its Equation

Equation of a circle: ((x - h)^2 + (y - k)^2 = r^2).
Center of circle (C) is represented by the ordered pair ((h, k)).
When the radius (r) equals zero, the graph becomes a single point.

Parabola Properties

Standard form of a parabola with vertex ((-3, -1)) and directrix (y = -\frac{3}{4}) is derived using the vertex and position of directrix.
The equation of a parabola can depend on its orientation and focus location.

Hyperbola Characteristics

The line segment joining the vertices of a hyperbola is known as the transverse axis.
The midpoint between the focus and the directrix is called the latus rectum.

Ellipse Equation and Properties

An ellipse centered at ((1, 2)) with a horizontal major axis can be expressed in standard form:
- Example: (\frac{(x-2)^2}{841} + \frac{(y-1)^2}{441} = 1).
Focal distance and lengths of major/minor axes contribute to the ellipse's equation.

Hyperbola Facts

Hyperbolas are asymmetric along the transverse axis with vertices located on the conjugate axis.
Asymptotes are straight lines that outline the behavior of a hyperbola.

General Concepts

Understanding the vertices, foci, directrices, and axes of conic sections is crucial.
Familiarity with the standard forms of equations assists in graphing and solving conic-related problems.

Description

Prepare for the 1st Quarter Prelim Exam at Moonwalk National High School. This quiz covers essential topics that are essential for Senior High School students in the first semester of the academic year 2024-2025. Focus on key subjects and concepts to excel in your exams.