SpletThe equation of the circle P is given by x2 + y2 – 4x + 6y – 12 = 0. (a) Find the coordinates of its center and radius. (b) Find the perpendicular distance from the centre of P to the line 3x + 4y = k in terms of k, where k is a … Splet10. jan. 2024 · The equation of the circle which is touching the above tangent at point (1,-1) is: ⇒ (x – 1) 2 + (y + 1) 2 + λ (3x – 4y – 7) = 0 ---- (1) Where λ ∈ R The required circle passes through the point (4, 0). ⇒ (4 – 1) 2 + (0 + 1) 2 + λ (3 × 4 – 4 × 0 – 7) = 0 ⇒ 9 + 1 + λ (5) = 0 ⇒ λ = -2 On substituting λ = -2 in Equation (1),
7. Show that the line 3x+4y+7=0 touches the circle …
SpletNow that we have a quadratic equation, we solve for the discriminant to determine whether it’s positive, negative, or zero: Discriminant = b^2 - 4ac = (-66)^2 - 4 (25) (36) = 4356 - 3600 = 756 Because the discriminant is positive, the line not only “touches” the circle, but intersects it at two points; see below. Continue Reading Anthony Madden Splet30. mar. 2024 · Ex 11.1, 7 Find the centre and radius of the circle x2 + y2 – 4x – 8y – 45 = 0 Given x2 + y2 – 4x – 8y – 45 = 0. We need to make this in form (x – h)2 + (y – k)2 = r2 From (1) x2 – 4x + y2 – 8y = 45 (x2 – 2 (x) (2)) + (y2 – 2 (y) (4)) = … cindy hochstetler
The line 4x + 6y + 9 = 0 touches the parabola y^2 = 4ax …
SpletA circle centered at the origin contains the point (0, -9). Does (8, root of 17) also lie on the circle? ... Yes, the distance from the origin to the point (8, root of 17) is 9 units. Consider a circle whose equation is x2 + y2 + 4x - 6y - 36 = 0. Which statements are true? Check all that apply. To complete the square for the x terms, add 4 to ... SpletSlope of a curve y = x2 − 3 at the point where x = 1 ? First you need to find f '(x), which is the derivative of f (x). Second, substitute in the value of x, in this case x = 1. The slope of the curve y = x2 − 3 at the x value of 1 is 2. SpletStraight Line and Circle - Free download as PDF File (.pdf), Text File (.txt) or read online for free. Time Limit : 6 Sitting Each of 75 Minutes duration approx. Select the correct … cindy hill seabrook tx