Class 9 Maths Quiz

Circle Equation

• The equation of a circle with center (a, b) and radius r is (x - a)^2 + (y - b)^2 = r^2
• The equation of the circle with center at (-2, 3) and radius 5 is (x + 2)^2 + (y - 3)^2 = 5^2
• The equation of the circle with center at (-2, 3) and radius 5 is (x + 2)^2 + (y - 3)^2 = 25

Slope of a Line

• The equation 3x - 4y = 12 is a linear equation in standard form
• The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept
• To find the slope of the line, rewrite the equation in slope-intercept form: 4y = 3x - 12
• Divide both sides by 4: y = (3/4)x - 3
• The slope of the line is 3/4

Quadratic Equations

• The equation 2x^2 - 5x + 2 = 0 is a quadratic equation in standard form
• The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the equation
• In the equation 2x^2 - 5x + 2 = 0, a = 2, b = -5, and c = 2
• Apply the quadratic formula: x = (5 ± √((-5)^2 - 4(2)(2))) / 2(2)
• Simplify the expression: x = (5 ± √(25 - 16)) / 4
• Simplify the expression: x = (5 ± √9) / 4
• Simplify the expression: x = (5 ± 3) / 4
• The solutions to the equation are x = (5 + 3) / 4 = 2 and x = (5 - 3) / 4 = 1/2