The angle can be calculated using the slopes derived from the equation, leading to 90 degrees.

By completing the square, we can find the slopes of the lines and calculate the angle between them.

The slopes are m1 = 2 and m2 = -0.5. The angle θ is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)| = |(2 + 0.5) / (1 - 1)|, which is undefined, indicating 90 degrees.

The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan^(-1) |(m1 - m2) / (1 + m1*m2)| = tan^(-1)(5/0) = 90 degrees.

The area of a circle is given by A = πr², so A = π(10)² = 100π.

The area of a circle is given by A = πr², so A = π(7)² = 49π.

The area of an ellipse is given by A = πab. Here, A = π * 7 * 4 = 28π.

Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.

The axis of symmetry for a parabola in the form y^2 = 4px is the x-axis, which is x = 0.

The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by x = -b/(2a). Here, a = -2, b = 4, so x = -4/(2*-2) = 1.

The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by x = -b/(2a). Here, a = 3 and b = 6, so x = -6/(2*3) = -1.

Both lines can be rewritten in slope-intercept form. The first line has slope -2/3 and the second line has the same slope, hence they are parallel.

The condition for the lines to be parallel is given by h^2 = ab.

The lines are coincident if the discriminant D of the quadratic equation is zero.

The condition for parallel lines is that the determinant of the coefficients must be zero.

Two lines are parallel if their coefficients of x and y are proportional, which means c1 must equal c2.

Two lines are parallel if their slopes are equal, i.e., m1 = m2.

Two lines are perpendicular if the product of their slopes m1 and m2 is -1.

The standard form of a parabola is (y - k)^2 = 4p(x - h). Here, p = 2, so the directrix is x = -2.

For the parabola y^2 = 4px, here 4p = 8, so p = 2. The directrix is x = -p = -2.

The distance between centers (1, 2) and (-3, -4) is calculated using the distance formula.

The distance between the foci is 6, calculated using the formula 2c where c = √(a^2 - b^2).

The distance between the foci is given by 2c, where c = √(a^2 - b^2) = √(25 - 16) = 3, so the total distance is 2c = 6.

Distance = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5.

Distance = |3(1) + 4(2) - 10| / √(3² + 4²) = |3 + 8 - 10| / 5 = 1.

Distance = |2(3) + 3(4) - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13.

The eccentricity e of a hyperbola is given by e = √(1 + b^2/a^2).

Using the standard form, the equation is (x + 1)² + (y - 2)² = 4² = 16.

The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

The equation of a circle with center at (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.