For the parabola (y - 2) squared equals 12(x + 5), where are the endpoints of the latus rectum?

1. The form is (y - k) squared equals 4p(x - h), so the axis of symmetry is parallel to the x-axis. 2. Reading off h and k gives the vertex (-5, 2). 3. Setting 4p equal to 12 gives p equal to 3, and since p is positive the curve opens right. 4. The focus is (h + p, k), which is (-2, 2). 5. The latus rectum runs through the focus parallel to the directrix, so its endpoints are (h + p, k plus or minus 2p). 6. Here 2p is 6, so the endpoints are (-2, 2 + 6) and (-2, 2 - 6). 7. That gives (-2, 8) and (-2, -4). 8. The pair (-2, 5) and (-2, -1) uses p instead of 2p for the half-length. 9. The pair (-8, 2) and (4, 2) runs the segment along the axis of symmetry, not across it. 10. The pair (1, 2) and (-11, 2) measures 2p sideways from the vertex instead of from the focus. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.3 The Parabola_