Area Under Curve
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Questions and Answers

What is the equation of the tangent line at the origin for the curve y = x² - x?

  • x + y = 1
  • x - y = 0
  • x + y = 0 (correct)
  • y = x

    • What is the x-intercept of the curve y = x² - x?

  • (0, 1) and (1, 0)
  • (0, 0) and (2, 0)
  • (1, 0) and (2, 0)
  • (0, 0) and (1, 0) (correct)

    • What is the y-intercept of the curve y = x² - x?

  • (0, 0) only (correct)
  • (0, 0) and (0, 1)
  • (1, 0) and (0, 0)
  • (0, 0) and (0, 2)

    • What is the axis of symmetry for the parabola y = 8x?

    <p>x = 0</p> Signup and view all the answers

    What is the point of local minima for the curve y = x² - x?

    <p>x = 1</p> Signup and view all the answers

    What is the condition for a curve to pass through the origin?

    <p>The equation of the curve contains no constant term</p> Signup and view all the answers

    What do the points of intersection of the curve with the axes represent?

    <p>The points where the curve cuts the axes</p> Signup and view all the answers

    What is the condition for a tangent line to be parallel to the x-axis?

    <p>dy/dx = 0</p> Signup and view all the answers

    What is the method to find the region of the curve?

    <p>Write the equation in the form y = f(x) and find the minimum and maximum values of x</p> Signup and view all the answers

    What is the condition for the curve to not exist in a region?

    <p>The value of y is imaginary</p> Signup and view all the answers

    What can be said about the curve represented by the equation y^2 = 4ax when x is negative?

    <p>It does not exist.</p> Signup and view all the answers

    What is the first step in finding the region represented by a linear inequality ax + by ≤ c?

    <p>Convert the inequality into equality to obtain a linear equation in x, y.</p> Signup and view all the answers

    What is the equation of a circle with centre at the origin and radius r?

    <p>x^2 + y^2 = r^2</p> Signup and view all the answers

    What is the method to find the points where a straight line meets with the coordinate axes?

    <p>By putting x = 0 and y = 0 respectively in its equation.</p> Signup and view all the answers

    What can be said about the curve represented by the equation a^2y^2 = x^2(a - x) when x > a?

    <p>It does not exist.</p> Signup and view all the answers

    What is the region represented by the inequality 3x + 4y ≤ 12?

    <p>The region that contains the origin</p> Signup and view all the answers

    What is the equation of the tangent at the origin for the curve y = x² - x?

    <p>x + y = 0</p> Signup and view all the answers

    What is the vertex of the parabola y = 8x?

    <p>(0, 0)</p> Signup and view all the answers

    What is the x-intercept of the curve y = x² - x?

    <p>Both (0, 0) and (1, 0)</p> Signup and view all the answers

    What is the focus of the parabola y = 8x?

    <p>(2, 0)</p> Signup and view all the answers

    What is the purpose of finding the points where a straight line meets with the coordinate axes?

    <p>To graph a straight line</p> Signup and view all the answers

    What is the effect of a negative value of x on the curve represented by the equation y² = 4ax?

    <p>The curve does not exist on the left side of the y-axis</p> Signup and view all the answers

    What is the next step after converting a linear inequality into equality to obtain a linear equation in x, y?

    <p>Draw the straight line represented by it</p> Signup and view all the answers

    What is the equation of a circle having centre at (0,0) and radius r, in terms of x and y?

    <p>x² + y² = r²</p> Signup and view all the answers

    What is the region represented by a linear inequality divided into after drawing the straight line?

    <p>Two unequal parts</p> Signup and view all the answers

    What is the condition for a curve to pass through the origin?

    <p>The equation of the curve does not contain constant terms</p> Signup and view all the answers

    How do you find the points of intersection of a curve with the x-axis?

    <p>By putting y = 0 in the equation of the curve</p> Signup and view all the answers

    What does the point of intersection of a curve with the x-axis represent?

    <p>The point where the curve intersects the x-axis</p> Signup and view all the answers

    What is the condition for a tangent line to be parallel to the x-axis?

    <p>The slope of the tangent line is zero</p> Signup and view all the answers

    What do you do to find the region of a curve?

    <p>Write the given equation as y = f(x) and find minimum and maximum values of x</p> Signup and view all the answers

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