Rui Baldwin

2020-10-25

Consider the equation:

a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola?

b) Use a rotation of axes to eliminate the xy-term. (Write an equation in XY-coordinates. Use a rotation angle that satisfies

Caren

Skilled2020-10-26Added 96 answers

Step 1

We have given an equation,

the general Cartesian form of a conic section:

The discriminant is

(a) If

(b) If

(c) If

Step 2

On comparing the given equation with the general form of conic section, we get,

The discriminant is

So the equation is hyperbola.

Step 3

b) In such a case, the relation between coordinate (x, y) and new coordinates (x', y') is given by:

We shall find the value of x,y by these values.

On plugging these values in the equation we get,

22+64

When a cold drink is taken from a refrigerator, its temperature is 5 degree C. After 25 minutes in a 20 degree C room its temperature has increased to 10 degree C. What is the temperature of the drink after 50 minutes?

How many minutes are there in $2\frac{3}{5}$ hours?

Find the answer for $64$ power $\frac{1}{6}$.

The following law describes the relationship between gas volume and pressure: ________. A)Boyle's law; B)Henry's law; C)Charles' law; D)Dalton's law

If an electric switch is open then no current flows through the circuit.

A)True;

B)FalseThe price elasticity of supply of a good is 0.8. Its price rises by 50 per cent. Calculate the percentage increase in its supply.

How many quarts are in 10 gallons?

When the net force acting on an object is zero, the total momentum of the system will:

A)remain constant;

B)increase with time;

C)decrease with time;

D)None of theseHow many centimeters are in four meters?

A notebook computer has a mass of 2.25 kilograms. About how many pounds does the notebook weigh?

If the dot product of two non-zero vectors is zero, then the vectors A)are parallel to each other. B)are perpendicular to each other. C)can have any orientation. D)are anti-parallel to each other.

Which is longer 5 miles or 10 kilometers?

9 grams is how many milligrams?

How to write $673.5$ in scientific notation?