Subject: Mathematics
Book: Maths Mastery
To rewrite conics in standard form, group x and y terms, complete the square for each. For instance, x² + 6x + y² – 2y= 6 transforms into (x²+6x+9)+(y²–2y+1)=6+9+1 → (x+3)²+(y–1)²=16, a circle. This systematically reveals center, radius (circle), or center, axes (ellipse, hyperbola). Completing the square is essential for identifying conic type, orientation, and focal properties. Mastery ensures quick conversions from general to standard forms, enabling geometric interpretations or direct application in advanced designs and analyses.
What is the square root of 144?
View QuestionIf x - y = 5 and x + y = 15, what is the value of x?
View QuestionIf x = 3 and y = 4, what is the value of x^2 + y^2?
View QuestionIf a:b = 3:4 and b:c = 5:6, what is a:c?
View QuestionIf sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?
View QuestionThe angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?
View QuestionThe LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?
View QuestionIf a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?
View QuestionA sphere has a radius of 7 cm. What is its volume?
View QuestionIf the probability of an event is 1/4, what is the probability of its complement?
View Question