Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)



Answer to a math question Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)

Expert avatar
45 Answers
First, find the derivative of the curve to get the slope of the tangent line. y = x² + 4x - 3 y' = 2x + 4 Evaluate the derivative at the point (1, 2) to find the slope of the tangent line at that point. y'(1) = 2(1) + 4 = 2 + 4 = 6 So, the slope of the tangent line at (1, 2) is 6. The slope of the normal line will be the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is -1/6. Now that you have the slope of the normal line and the point (1, 2), you can use the point-slope form of a line to find the equation of the normal line: y - y₁ = m(x - x₁) Where: (x₁, y₁) = (1, 2) m = -1/6 (slope of the normal line) Now, plug in the values: y - 2 = (-1/6)(x - 1) Multiply both sides by 6 to eliminate the fraction: 6(y - 2) = -1(x - 1) 6y - 12 = -x + 1 Now, rearrange the equation to get it in standard form: x + 6y = 13

Frequently asked questions (FAQs)
What are the characteristics of a circle defined by the equation x^2 + y^2 = r^2? Explain the meaning of each term and how they determine the shape and properties of the circle.
What is the median of a set of numbers: 2, 4, 6, 7, 9?
What is the resultant vector when a vector of magnitude 5 in the positive x-direction is subtracted from a vector of magnitude 8 in the positive y-direction? (
New questions in Mathematics
How much volume of water in MegaLiters (ML) is required to irrigate 30 Hectare crop area with depth of 20mm?
Determine all solutions to the inequality |2x + 6| − |x + 1| < 6. Write your final answer in interval notation
I need .23 turned into a fraction
Determine the equations of the recipes that pass through the following pairs of points P1 (2;-1) and p2 (4;-1)
A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.
In the telephone exchange of a certain university, calls come in at a rate of 5 every 2 minutes. Assuming a Poisson distribution, the average number of calls per second is: a) 1/8 b) 1/12 c) 1/10 d) 2/5 e) 1/24
A triangular window has a base of 6 ft. and a height of 7 ft. What is its area?
The market for economics textbooks is represented by the following supply and demand equations: P = 5 + 2Qs P = 20 - Qd Where P is the price in £s and Qs and Qd are the quantities supplied and demanded in thousands. What is the equilibrium price?
19) If the temperature of -8°C decreases by 12°C, how much will it be? a)-20°C -4°C c) 4°C d) 20°C
The simple average of 15 , 30 , 40 , and 45 is
The question is using rule 72 determine Kari wants to save 10,000 for a down payment on a house. Illustrate the difference in years it will take her to double her current 5,000 savings based on 6%, 12% and 18% interest rate .
Calculate the difference between 407 and 27
Twenty‐five students in a class take a test for which the average grade is 75. Then a twenty‐sixth student enters the class, takes the same test, and scores 70. The test average grade calculated with 26 students will
Kaya deposits 25,000 into an account that earns 3% interest compounded monthly. How much does Kaya have in the account after 6 years 8 months? Round to the nearest cent. 32,912.50 30,000 29,923.71 30,527.45
Translate to an equation and solve. Let x be the unknown number: What number is 52% of 81.
For how long does the principal amount of €7,537 bring the same interest as the principal amount of €12,345 invested for 8 months? Interest calculation is simple and decursive.
How many digits are there in Hindu-Arabic form of numeral 26 × 1011
Slope (7,3) and (9,5)