Formulae

Question 1

What is the Distance Formula?

Answer 1

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Question 2

What is the Section Formula for Internal Division?

Answer 2

(mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)

Question 3

What is the Section Formula for External Division?

Answer 3

(mx₂ - nx₁)/(m-n), (my₂ - ny₁)/(m-n)

Question 4

What is the Midpoint Formula?

Answer 4

(x₁ + x₂)/2, (y₁ + y₂)/2

Question 5

What is the formula for the Centroid of a Triangle?

Answer 5

(x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3

Question 6

What is the formula for the Incentre of a Triangle?

Answer 6

(ax₁ + bx₂ + cx₃)/(a+b+c), (ay₁ + by₂ + cy₃)/(a+b+c)

Question 7

What is the Area of a Triangle formula?

Answer 7

A = 1/2 | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |

Question 8

How do you calculate the Slope of a Line?

Answer 8

m = (y₂ - y₁)/(x₂ - x₁)

Question 9

What is the Point-Slope Form of the Equation of a Line?

Answer 9

y - y₁ = m(x - x₁)

Question 10

What is the Slope-Intercept Form of the Equation of a Line?

Answer 10

y = mx + c

Question 11

What is the Two-Point Form of the Equation of a Line?

Answer 11

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

Question 12

What is the Intercept Form of the Equation of a Line?

Answer 12

(x/a) + (y/b) = 1

Question 13

How do you find the Angle Between Two Lines?

Answer 13

tan θ = |(m₁ - m₂)/(1 + m₁m₂)|

Question 14

What is the condition for Parallel Lines?

Answer 14

m₁ = m₂

Question 15

What is the condition for Perpendicular Lines?

Answer 15

m₁ × m₂ = -1

Question 16

What is the Standard Form of a Circle Equation?

Answer 16

(x - h)² + (y - k)² = r²

Question 17

What is the General Form of a Circle Equation?

Answer 17

x² + y² + 2gx + 2fy + c = 0

Question 18

What is the equation of a Parabola?

Answer 18

y² = 4ax

Question 19

What is the equation of an Ellipse?

Answer 19

(x²/a²) + (y²/b²) = 1

Question 20

What is the equation of a Hyperbola?

Answer 20

(x²/a²) - (y²/b²) = 1

Question 21

What does Locus of a Point represent?

Answer 21

The equation representing the path traced by a moving point

Question 22

What is the General Equation of a Line?

Answer 22

Ax + By + C = 0

Question 23

How do you find the Length of Perpendicular from a Point to a Line?

Answer 23

d = |Ax₁ + By₁ + C|/√(A² + B²)

Question 24

What is the formula for Distance Between Two Parallel Lines?

Answer 24

d = |C₁ - C₂|/√(A² + B²)

Question 25

What is the Equation of Family of Lines Passing Through the Intersection of Two Lines?

Answer 25

L₁ + λL₂ = 0

Question 26

What is the Parametric Form of a Circle Equation?

Answer 26

x = h + r cos θ, y = k + r sin θ

Question 27

What is the Length of the Chord formula?

Answer 27

Length = 2√(r² - d²)

Question 28

What is the Eccentricity of a Conic Section?

Answer 28

e = c/a

Question 29

What is the Eccentricity value for a Circle?

Answer 29

e = 0

Question 30

What is the Eccentricity value for a Parabola?

Answer 30

e = 1

Question 31

What is the Eccentricity condition for an Ellipse?

Answer 31

e < 1

Question 32

What is the Eccentricity condition for a Hyperbola?

Answer 32

e > 1

Question 33

What is the Focus and Directrix for a Parabola?

Answer 33

Focus (a, 0), Directrix x = -a

Question 34

What are the Foci and Directrices for an Ellipse?

Answer 34

Foci (±c, 0), Directrices x = ±(a/e)

Question 35

What are the Foci and Directrices for a Hyperbola?

Answer 35

Foci (±c, 0), Directrices x = ±(a/e)

Question 36

What are the Polar Coordinates Conversion formulas?

Answer 36

x = r cos θ, y = r sin θ

Question 37

What is the Equation of Pair of Lines?

Answer 37

ax² + 2hxy + by² = 0

Question 38

What is the formula for Angle Between Pair of Lines?

Answer 38

tan θ = (2√(h² - ab))/(a + b)

Question 39

What is the equation for a Rectangular Hyperbola?

Answer 39

xy = c²

Question 40

What is the equation of the Director Circle?

Answer 40

x² + y² = a² - b²

Question 41

What are the Asymptotes of a Hyperbola?

Answer 41

(x/a) ± (y/b) = 0

Question 42

What is the equation of a Conjugate Hyperbola?

Answer 42

(x²/b²) - (y²/a²) = 1