30 Questions
What is the equation of the tangent line at the origin for the curve y = x² - x?
x + y = 0
What is the x-intercept of the curve y = x² - x?
(0, 0) and (1, 0)
What is the y-intercept of the curve y = x² - x?
(0, 0) only
What is the axis of symmetry for the parabola y = 8x?
x = 0
What is the point of local minima for the curve y = x² - x?
x = 1
What is the condition for a curve to pass through the origin?
The equation of the curve contains no constant term
What do the points of intersection of the curve with the axes represent?
The points where the curve cuts the axes
What is the condition for a tangent line to be parallel to the x-axis?
dy/dx = 0
What is the method to find the region of the curve?
Write the equation in the form y = f(x) and find the minimum and maximum values of x
What is the condition for the curve to not exist in a region?
The value of y is imaginary
What can be said about the curve represented by the equation y^2 = 4ax when x is negative?
It does not exist.
What is the first step in finding the region represented by a linear inequality ax + by ≤ c?
Convert the inequality into equality to obtain a linear equation in x, y.
What is the equation of a circle with centre at the origin and radius r?
x^2 + y^2 = r^2
What is the method to find the points where a straight line meets with the coordinate axes?
By putting x = 0 and y = 0 respectively in its equation.
What can be said about the curve represented by the equation a^2y^2 = x^2(a - x) when x > a?
It does not exist.
What is the region represented by the inequality 3x + 4y ≤ 12?
The region that contains the origin
What is the equation of the tangent at the origin for the curve y = x² - x?
x + y = 0
What is the vertex of the parabola y = 8x?
(0, 0)
What is the x-intercept of the curve y = x² - x?
Both (0, 0) and (1, 0)
What is the focus of the parabola y = 8x?
(2, 0)
What is the purpose of finding the points where a straight line meets with the coordinate axes?
To graph a straight line
What is the effect of a negative value of x on the curve represented by the equation y² = 4ax?
The curve does not exist on the left side of the y-axis
What is the next step after converting a linear inequality into equality to obtain a linear equation in x, y?
Draw the straight line represented by it
What is the equation of a circle having centre at (0,0) and radius r, in terms of x and y?
x² + y² = r²
What is the region represented by a linear inequality divided into after drawing the straight line?
Two unequal parts
What is the condition for a curve to pass through the origin?
The equation of the curve does not contain constant terms
How do you find the points of intersection of a curve with the x-axis?
By putting y = 0 in the equation of the curve
What does the point of intersection of a curve with the x-axis represent?
The point where the curve intersects the x-axis
What is the condition for a tangent line to be parallel to the x-axis?
The slope of the tangent line is zero
What do you do to find the region of a curve?
Write the given equation as y = f(x) and find minimum and maximum values of x
Learn how to graph linear inequalities and parabolas, including finding the region represented by the inequality and identifying the vertex and focus of a parabola.
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