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A circle with centre (-2, 4) passes through the point A(n, 1). Given that the tangent o the circle at A has a gradient of 3, find the value of n. n = A circle has the equation x² + y² + 6ax - 7y - 2 = 0, where a is a constant. Find the centre and radius of the circle in terms of a. Centre = ( ), Radius=

A circle with centre (-2, 4) passes through the point A(n, 1). Given that the tangent o the circle at A has a gradient of 3, find the value of n. n = A circle has the equation x² + y² + 6ax - 7y - 2 = 0, where a is a constant. Find the centre and radius of the circle in terms of a. Centre = ( ), Radius=

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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11:31 Fri 10 Mar < x Untitled Notebook (2) po a) n = a = Given f(x) = e2x a) Maths Tutorial Untitled Notebook (3) c) Given the point (3,-1) lies on the circle, find the value of a. - A circle with centre (−2, 4) passes through the point A(n, 1). Given that the tangent to the circle at A has a gradient of , find the value of n. ●●● b) A circle has the equation x² + y² + 6ax − 7y - ³ = 0, where a is a constant. - Find the centre and radius of the circle in terms of a. Centre = ( ), Radius = Determine the range of f(x). f(x) > X = 4, x € R, g(x) = X T b) Find an expression for the inverse function f-¹(x). f-¹(x) = V Mastering Chemistry O** C) Solve the equation g(f(x)) = 1 for x and give your answer in terms of In(2). of the A, B and M 3=( 1 x-11, x = R₁ x ‡ 11. ER, # x k is a constant, to inimum point at Mar of the points M and Y=( Untitled Notebook (3) ²-6x+16,x ef f(x) = (x + a)²+b. 24% 0 1 for x and give y ion for the inverse fun age of f(x).
Transcribed Image Text:11:31 Fri 10 Mar < x Untitled Notebook (2) po a) n = a = Given f(x) = e2x a) Maths Tutorial Untitled Notebook (3) c) Given the point (3,-1) lies on the circle, find the value of a. - A circle with centre (−2, 4) passes through the point A(n, 1). Given that the tangent to the circle at A has a gradient of , find the value of n. ●●● b) A circle has the equation x² + y² + 6ax − 7y - ³ = 0, where a is a constant. - Find the centre and radius of the circle in terms of a. Centre = ( ), Radius = Determine the range of f(x). f(x) > X = 4, x € R, g(x) = X T b) Find an expression for the inverse function f-¹(x). f-¹(x) = V Mastering Chemistry O** C) Solve the equation g(f(x)) = 1 for x and give your answer in terms of In(2). of the A, B and M 3=( 1 x-11, x = R₁ x ‡ 11. ER, # x k is a constant, to inimum point at Mar of the points M and Y=( Untitled Notebook (3) ²-6x+16,x ef f(x) = (x + a)²+b. 24% 0 1 for x and give y ion for the inverse fun age of f(x).
11:33 Fri 10 Mar < x Untitled Notebook (2) Po For a quadratic function f(x) = x² − 6x + 16, x € R M = ( y CD A(2,0) M (3,-6) y = f(x) Untitled Notebook (3) Maths Tutorial a) Express f(x) in the form of ƒ(x) = (x + a)² + b, where a and b are constants. f(x)= B (10,0) b) The graph of f(x) has a minimum point at M and meets the y-axis at Y. Write down the coordinates of the points M and Y. ), Y= ( > x ●●● ) c) The graph of f(x) + k, where k is a constant, touches the x-axis. Find the value of k. k = x T The curve crosses the x axis at A(2, 0) and at the point B(10, 0). The curve has a minimum at M(3, −6). ), B = ( V Mastering Chemistry XO ), M=( a) Write down the co-ordinate of A, B and M under the tranformation y = ƒ(2x). A= ( ), B = ( ), M = ( b) Write down the co-ordinates of the A, B and M under the transformation y = -2f(x) + 3. A = ( 3 ) ) of the A, B and M B=( X Untitled Notebook (3) k is a constant, to inimum point at Mar of the points M and Y=( x²-6x+16, xel 23% 0 f(x) = (x + a)²+b.w 1 for x and give y ion for the inverse fune
Transcribed Image Text:11:33 Fri 10 Mar < x Untitled Notebook (2) Po For a quadratic function f(x) = x² − 6x + 16, x € R M = ( y CD A(2,0) M (3,-6) y = f(x) Untitled Notebook (3) Maths Tutorial a) Express f(x) in the form of ƒ(x) = (x + a)² + b, where a and b are constants. f(x)= B (10,0) b) The graph of f(x) has a minimum point at M and meets the y-axis at Y. Write down the coordinates of the points M and Y. ), Y= ( > x ●●● ) c) The graph of f(x) + k, where k is a constant, touches the x-axis. Find the value of k. k = x T The curve crosses the x axis at A(2, 0) and at the point B(10, 0). The curve has a minimum at M(3, −6). ), B = ( V Mastering Chemistry XO ), M=( a) Write down the co-ordinate of A, B and M under the tranformation y = ƒ(2x). A= ( ), B = ( ), M = ( b) Write down the co-ordinates of the A, B and M under the transformation y = -2f(x) + 3. A = ( 3 ) ) of the A, B and M B=( X Untitled Notebook (3) k is a constant, to inimum point at Mar of the points M and Y=( x²-6x+16, xel 23% 0 f(x) = (x + a)²+b.w 1 for x and give y ion for the inverse fune
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