3.1.38 Curves of the 2nd order
condition: Determine the semimajor axis of the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{144}=1 \), if the line passing through its left focus is perpendicular to the line \( x+2 y+1=0 \) and passes through point \( A(-2,6) \).
Study of curves of the second order and their characteristics. Ellipse, hyperbola, parabola. Finding eccentricities, foci, focal radii, major and minor axes, including imaginary, canonical equations and plotting.